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In geometry, a polyhedron (pl.: polyhedra or polyhedrons; from Greek πολύ (poly-)  'many' and ἕδρον (-hedron)  'base, seat') is a three-dimensional figure...

more specifically in polyhedral combinatorics, a Goldberg polyhedron is a convex polyhedron made from hexagons and pentagons. They were first described...

Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical...

polyhedra. They are 2 infinite classes of prisms and antiprisms, the convex polyhedrons as in 5 Platonic solids and 13 Archimedean solids—2 quasiregular and...

A geodesic polyhedron is a convex polyhedron made from triangles which approximates a sphere. They usually have icosahedral symmetry, such that they have...

A polyhedron model is a physical construction of a polyhedron, constructed from cardboard, plastic board, wood board or other panel material, or, less...

regular polyhedron is a polyhedron with regular and congruent polygons as faces. Its symmetry group acts transitively on its flags. A regular polyhedron is...

between the small and medium polyhedrons (2), between the medium and the large polyhedrons (3) and outside the large polyhedron (4). Computer Generated Imagery...

Szilassi polyhedron is a nonconvex polyhedron, topologically a torus, with seven hexagonal faces. The tetrahedron and the Szilassi polyhedron are the only...

called a polyhedron; for this concept see n-dimensional polyhedron. Polyhedron may also refer to: Polyhedron (magazine), formerly Polyhedron Newszine...

An n-dimensional polyhedron is a geometric object that generalizes the 3-dimensional polyhedron to an n-dimensional space. It is defined as a set of points...

Leonardo polyhedron is a polyhedron with a Platonic solid's rotational symmetry and genus g ≥ 2 {\displaystyle g\geq 2} . Here, a polyhedron is the unbounded...

In geometry, every polyhedron is associated with a second dual structure, wherein the vertices of one correspond to the faces of the other and the edges...

"sides" meeting at one place. A vertex is a corner point of a polygon, polyhedron, or other higher-dimensional polytope, formed by the intersection of edges...

elongated square gyrobicupola or pseudo­rhombi­cub­octa­hedron is an extra polyhedron with regular faces and congruent vertices. Still, it is not generally...

In geometry, a net of a polyhedron is an arrangement of non-overlapping edge-joined polygons in the plane that can be folded (along edges) to become the...

geometry, the Császár polyhedron (Hungarian: [ˈt͡ʃaːsaːr]) is a nonconvex toroidal polyhedron with 14 triangular faces. This polyhedron has no diagonals;...

In geometry, a Kepler–Poinsot polyhedron is any of four regular star polyhedra. They may be obtained by stellating and faceting the regular convex dodecahedron...

Teacher (March 1963). The World of Polyhedrons The Mathematics Teacher (March 1965). Some Facts About Uniform Polyhedrons. Summation: Association of Teachers...

volumes of various solids, including pyramids, prisms, cubes (and other polyhedrons), cylinders, cones (including truncated) and other solids of revolution...

Psychedelic Polyhedron is the second album by Mainliner, released in April 1997 by Fractal Records. All lyrics are written by Asahito Nanjo; all music...

4-dimensional space https://levskaya.github.io/polyhedronisme/ a generator of polyhedrons and Conway operations applied to them, including Johnson solids....

An orthogonal polyhedron is a polyhedron in which all edges are parallel to the axes of a Cartesian coordinate system, resulting in the orthogonal faces...

truncated icosahedron is a polyhedron that can be constructed by truncating all of the regular icosahedron's vertices. The polyhedron can be regarded as a football...

In geometry, a uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i...

In geometry, a Schönhardt polyhedron is a polyhedron with the same combinatorial structure as a regular octahedron, but with dihedral angles that are non-convex...

classically defined for the surface of a three-dimensional polyhedron. If the polyhedron has V vertices (corners), E edges, and F faces, then the Euler...

In mathematics, especially several complex variables, an analytic polyhedron is a subset of the complex space Cn of the form P = { z ∈ D : | f j ( z )...

In geometry, an octahedron (pl.: octahedra or octahedrons) is any polyhedron with eight faces. One special case is the regular octahedron, a Platonic solid...

dual uniform polyhedron is the dual of a uniform polyhedron. Where a uniform polyhedron is vertex-transitive, a dual uniform polyhedron is face-transitive...

In geometry, a spherical polyhedron or spherical tiling is a tiling of the sphere in which the surface is divided or partitioned by great arcs into bounded...

In geometry, a composite polyhedron is a convex polyhedron that produces two convex, regular-faced polyhedra when sliced by a plane.[dubious – discuss]...

dimension 2 (a plane tiling) or higher, or a polytope of dimension 3 (a polyhedron) or higher, is isohedral or face-transitive if all its faces are the same...

In geometry, a prism is a polyhedron comprising an n-sided polygon base, a second base which is a translated copy (rigidly moved without rotation) of the...

dodecahedron is a polyhedron with twelve pentagonal faces, thirty edges, and twenty vertices. It is one of the Platonic solids, a set of polyhedrons in which the...

uniform polyhedra, the cubohemioctahedron and octahemioctahedron. These polyhedrons are constructed from the skeleton of a cuboctahedron in which the four...

semiregular polyhedron (or semiregular polytope) is used variously by different authors. In its original definition, it is a polyhedron with regular...

resulting polyhedron has 20 equilateral triangles, 30 squares, and 10 regular pentagons as its faces. The difference between those two polyhedrons is that...

discovered around 1990 by the mathematician Steve Waterman. A Waterman polyhedron is created by packing spheres according to the cubic close(st) packing...

In geometry, a toroidal polyhedron is a polyhedron which is also a toroid (a g-holed torus), having a topological genus (g) of 1 or greater. Notable examples...

have any dimension. The vertices, edges, and (2-dimensional) faces of a polyhedron are all faces in this more general sense. In elementary geometry, polyhedra...

convex polyhedron with 12 congruent rhombic faces. It has 24 edges, and 14 vertices of 2 types. As a Catalan solid, it is the dual polyhedron of the cuboctahedron...

{\vec {x}}_{t}(s,t))\cdot {\vec {v}}=0} . The intersection curve of two polyhedrons is a polygon (see intersection of three houses). The display of a parametrically...

or intersphere of a convex polyhedron is a sphere which is tangent to every edge of the polyhedron. Not every polyhedron has a midsphere, but the uniform...

a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope. In a polygon, an edge is a line segment...

these edges form six square faces of the same size. It is an example of a polyhedron. It is a special case of a cuboid, a parallelepiped, and a rhombohedron...

dirhombidodecahedron, also called Skilling's figure, is a degenerate uniform star polyhedron. Its full realization has 204 faces (120 triangles, 60 squares, and 24...

Conway polyhedron notation, invented by John Horton Conway and promoted by George W. Hart, is used to describe polyhedra based on a seed polyhedron modified...

tetrahedron, which is the smallest possible number of faces and vertices a polyhedron can have. The regular tetrahedron, also called a 3-simplex, is the simplest...

polyhedron are extended indefinitely the space around the polyhedron is divided into unbounded sub spaces and often a number of bounded polyhedrons or...

In geometry, a flexible polyhedron is a polyhedral surface without any boundary edges, whose shape can be continuously changed while keeping the shapes...

while interior angles in a triangle add up to 180°. However, on a convex polyhedron, the angles of the faces meeting at a vertex add up to less than 360°...

icosahedron (/ˌaɪkɒsəˈhiːdrən, -kə-, -koʊ-/ or /aɪˌkɒsəˈhiːdrən/) is a polyhedron with 20 faces. The name comes from Ancient Greek εἴκοσι (eíkosi) 'twenty'...

on a vertex of this polyhedron or inside of it. It was studied by Max Brückner after the discovery of Kepler–Poinsot polyhedron. It can be viewed as...

uniform star polyhedron with Wythoff symbol of the form 3 | p q or ⁠3/2⁠ | p q are ditrigonal, at least if p and q are not 2. Each polyhedron includes two...

chamfer or edge-truncation is a topological operator that modifies one polyhedron into another. It separates the faces by reducing them, and adds a new...

In geometry, an n-gonal antiprism or n-antiprism is a polyhedron composed of two parallel direct copies (not mirror images) of an n-sided polygon, connected...

A pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle, called a lateral...

In geometry, a uniform polyhedron compound is a polyhedral compound whose constituents are identical (although possibly enantiomorphous) uniform polyhedra...

In geometry, a star polyhedron is a polyhedron which has some repetitive quality of nonconvexity giving it a star-like visual quality. There are two general...

In geometry, an omnitruncated polyhedron is a truncated quasiregular polyhedron. When they are alternated, they produce the snub polyhedra. All omnitruncated...

In geometry, a monostatic polytope or unistable polyhedron is a d {\displaystyle d} -polytope which "can stand on only one face". They were described in...

nontraditional, surrealist portrayal of the Crucifixion, it depicts Christ on a polyhedron net of a tesseract (hypercube). It is one of his best-known paintings...

duoprism. An octahedron is a regular polyhedron with eight equilateral triangles as faces. is the dual polyhedron to the cube and one of eight convex deltahedra...

In geometry, a polytope (for example, a polygon or a polyhedron) or a tiling is isotoxal (from Greek τόξον  'arc') or edge-transitive if its symmetries...

form a convex polyhedron called its convex hull. A compound is a faceting of its convex hull.[citation needed] Another convex polyhedron is formed by the...

a snub polyhedron is a polyhedron obtained by performing a snub operation: alternating a corresponding omnitruncated or truncated polyhedron, depending...

In geometry, the density of a star polyhedron is a generalization of the concept of winding number from two dimensions to higher dimensions, representing...

before the Big Bang, what? Holy Week has many colors, it's a very strange polyhedron [a multifaceted thing]. It is related to faith, popular religion and Andalusian...

In three-dimensional hyperbolic geometry, an ideal polyhedron is a convex polyhedron all of whose vertices are ideal points, points "at infinity" rather...

In geometry and polyhedral combinatorics, an integral polytope is a convex polytope whose vertices all have integer Cartesian coordinates. That is, it...

In geometry, a (globally) projective polyhedron is a tessellation of the real projective plane. These are projective analogs of spherical polyhedra – tessellations...

tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertices...

A Kokotsakis polyhedron is a polyhedral surface in three-dimensional space consisting of any polygon as its base and quadrilaterals alternating with triangles...

problem, which asks for a single polyhedron that tiles Euclidean 3-space, but such that no tessellation by this polyhedron is isohedral. Such anisohedral...

the truncated octahedron is a 6-zonohedron. It is also the Goldberg polyhedron GIV(1,1), containing square and hexagonal faces. Like the cube, it can...

an abstract, regular polyhedron, containing half the faces of a regular dodecahedron. It can be realized as a projective polyhedron (a tessellation of the...

The regular icosahedron (or simply icosahedron) is a convex polyhedron that can be constructed from a pentagonal antiprism by attaching two pentagonal...

In geometry, a regular octahedron is an eight-sided polyhedron with equilateral triangles as its faces. Known for its highly symmetrical form, the regular...

convex polyhedron), and is the smallest polyhedral graph that does not have a Hamiltonian cycle, a cycle passing through all its vertices. The polyhedron whose...

The rhombicuboctahedron or small rhombicuboctahedron is a polyhedron with 26 faces, consisting of 8 equilateral triangles and 18 squares. It was named...

In geometry, a space-filling polyhedron is a polyhedron that can be used to fill all of three-dimensional space via translations, rotations and/or reflections...

In geometry, Steffen's polyhedron is a flexible polyhedron discovered (in 1978) by and named after Klaus Steffen [de]. It is based on the Bricard octahedron...

example, a two-dimensional polygon is a 2-polytope and a three-dimensional polyhedron is a 3-polytope. In this context, "flat sides" means that the sides of...

hemispherical thin-shell structure (lattice-shell) based on a geodesic polyhedron. The rigid triangular elements of the dome distribute stress throughout...

determine the authenticity of remains thought to belong to Leonardo. Leonardo polyhedron Leonardo da Vinci's Notebooks General See Nicholl (2005, pp. 17–20) and...

Polyhedron no. 95 (1994) Centaur-Kin, Gnoat Polyhedron no. 95 (1994) Centaur-Kin, Ha'pony Polyhedron no. 95 (1994) Centaur-Kin, Zebranaur Polyhedron no...

tetrahedron is a polyhedron with four equilateral triangular faces. A regular tetrahedron is a tetrahedron (that is, a four-sided polyhedron) in which all...

Z-polyhedron or Z-polytope may refer to: The set of integer points in convex polyhedron Convex lattice polytope This disambiguation page lists articles...

polyhedron is a self-intersecting uniform polyhedron. They are also sometimes called nonconvex polyhedra to imply self-intersecting. Each polyhedron can...

Polyhedron (formerly Polyhedron Newszine) was a magazine targeting consumers of role-playing games, and originally the official publication of the RPGA...

projection based on a spherical polyhedron. Typically, the polyhedron is overlaid on the globe, and each face of the polyhedron is transformed to a polygon...

In geometry, the Hessian polyhedron is a regular complex polyhedron 3{3}3{3}3, , in C 3 {\displaystyle \mathbb {C} ^{3}} . It has 27 vertices, 72 3{} edges...

created by this system of spheres. Because of this restriction, some polyhedrons may not be included as a deltahedron: the triangular bipyramid (as forming...

The trapezo-rhombic dodecahedron is a polyhedron with six trapezoidal and six rhombic faces. This polyhedron can be obtained from a rhombic dodecahedron...

mathematician Willem Abraham Wythoff, is a method for constructing a uniform polyhedron or plane tiling. It is often referred to as Wythoff's kaleidoscopic construction...

In the geometry of numbers, the Klein polyhedron, named after Felix Klein, is used to generalize the concept of simple continued fractions to higher dimensions...

it can be described in terms of geometrically finite groups. A convex polyhedron C in hyperbolic space is called geometrically finite if its closure C...

Structure: A Source Book of Design. Dover Publications, Inc. ISBN 0-486-23729-X. (Section 3-7 to 3-9) Weisstein, Eric W. "Uniform Polyhedron". MathWorld....

geometry, a cuboid is a hexahedron with quadrilateral faces, meaning it is a polyhedron with six faces; it has eight vertices and twelve edges. A rectangular...

In geometry, a dodecahedron or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with...

Chazelle polyhedron is a non-convex polyhedron constructed by removing pieces of wedges from both top and bottom of a cube's sides, leaving the notches...

In geometry, the chamfered dodecahedron is a convex polyhedron with 80 vertices, 120 edges, and 42 faces: 30 hexagons and 12 pentagons. It is constructed...

truncated dodecahedron can be applied in the polyhedron's construction known as the augmentation. Examples of polyhedrons are the Johnson solids, whose constructions...

In geometry, the small stellated dodecahedron is a Kepler–Poinsot polyhedron, named by Arthur Cayley, and with Schläfli symbol {5⁄2, 5}. It is one of four...

In geometry, a polytope (e.g. a polygon or polyhedron) or a tiling is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries...

geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge. Informally, any sloping...

dodecahedron is a convex polyhedron with 12 congruent rhombi as its faces. The rhombic triacontahedron is a convex polyhedron with 30 golden rhombi (rhombi...

uniform star polyhedron some of whose faces pass through its center. These hemi-faces lie parallel to the faces of some other symmetrical polyhedron, and their...

In geometry, a regular skew apeirohedron is an infinite regular skew polyhedron. They have either skew regular faces or skew regular vertex figures. In...

hendecahedrons are cones, cylinders, some Jason polyhedrons, and the semi-regular polyhedron. The semi-regular polyhedron here is not the Archimedean solid, but...

infinite family of trapezohedra, face-transitive polyhedra. Its dual polyhedron is the pentagonal antiprism. As a decahedron it has ten faces which are...

In geometry, a prismatic uniform polyhedron is a uniform polyhedron with dihedral symmetry. They exist in two infinite families, the uniform prisms and...

In geometry, a quasiregular polyhedron is a uniform polyhedron that has exactly two kinds of regular faces, which alternate around each vertex. They are...

Metropolitan France for its resemblance to a regular hexagon A hexahedron is a polyhedron with six faces, with a cube being a special case Hexameter is a poetic...

In geometry, an icosidodecahedron or pentagonal gyrobirotunda is a polyhedron with twenty (icosi-) triangular faces and twelve (dodeca-) pentagonal faces...

alongside other uniform prisms, has 14 faces. The Szilassi polyhedron and its dual, the Császár polyhedron, are the simplest toroidal polyhedra; they have 14...

or insphere of a convex polyhedron is a sphere that is contained within the polyhedron and tangent to each of the polyhedron's faces. It is the largest...

In geometry, the truncated triakis tetrahedron is a convex polyhedron with 16 faces: four sets of three pentagons with a shared vertex, arranged in a tetrahedral...

Diameter Circumference Disk Area Three-dimensional Surface area Volume Polyhedron Platonic Solid Tetrahedron Reuleaux cuboid Cube Octahedron Dodecahedron...

rather than each quarter-turn. The regular dodecahedron and its dual polyhedron the icosahedron are Platonic solids whose dimensions are related to the...

hemicube is an abstract, regular polyhedron, containing half the faces of a cube. It can be realized as a projective polyhedron (a tessellation of the real...

A tetradecahedron is a polyhedron with 14 faces. There are numerous topologically distinct forms of a tetradecahedron, with many constructible entirely...

computational geometry, the star unfolding of a convex polyhedron is a net obtained by cutting the polyhedron along geodesics (shortest paths) through its faces...

morphism that is uniquely defined by its main property Canonical polyhedron, a polyhedron whose edges are all tangent to a common sphere, whose center is...

The rectification of any regular self-dual polyhedron or tiling will result in another regular polyhedron or tiling with a tiling order of 4, for example...

case of a three-dimensional simplicial polytope, known as the simplicial polyhedron, the polytope contains only triangular faces of any type. These polyhedra...

A noble polyhedron is one which is isohedral (all faces the same) and isogonal (all vertices the same). They were first studied in any depth by Edmund...

In geometry, a pentahexagonal pyritoheptacontatetrahedron is a near-miss Johnson solid with pyritohedral symmetry. This near-miss was discovered by Mason...

Commons has media related to Decahedra. In geometry, a decahedron is a polyhedron with ten faces. There are 32300 topologically distinct decahedra, and...

component with flat surfaces that refract light Prism (geometry), a kind of polyhedron Prism may also refer to: Prism (geology), a type of sedimentary deposit...

of a general n-polytope is sliced off. Take some corner or vertex of a polyhedron. Mark a point somewhere along each connected edge. Draw lines across the...

intersecting roof pitches. The elongated gyrobifastigium is the dual polyhedron of a snub disphenoid,[citation needed] one of 92 Johnson solids, sharing...

honeycomb is said to be a space-filling polyhedron. A necessary condition for a polyhedron to be a space-filling polyhedron is that its Dehn invariant must be...

geometry, a circumscribed sphere of a polyhedron is a sphere that contains the polyhedron and touches each of the polyhedron's vertices. The word circumsphere...

hollowing is based on a 3 dimensional homothety about the centre. Regular polyhedrons have similar ratios. The hollow cone is based on a scaling about the...

toroidal polyhedron with seven hexagonal faces, in which each pair of faces share an edge. The new construction was soon dubbed the Szilassi polyhedron. This...

A geodesic grid is a spatial grid based on a geodesic polyhedron or Goldberg polyhedron. The earliest use of the (icosahedral) geodesic grid in geophysical...

more generally, the set of points of an affine lattice, in a polyhedron is called Z-polyhedron, from the mathematical notation Z {\displaystyle \mathbb {Z}...

it is a Johnson solid, a convex polyhedron with regular faces. It can be used to construct many other polyhedrons, particularly other Johnson solids...

elongated triangular bipyramid or elongated triangular dipyramid is a polyhedron constructed from a triangular prism by attaching two regular tetrahedra...

cuboctahedron. The triangular cupola can be applied to construct many polyhedrons. The triangular cupola has four triangles, three squares, and one hexagon...

symbol is a notation representing a Wythoff construction of a uniform polyhedron or plane tiling within a Schwarz triangle. It was first used by Coxeter...

had already been given as an example of a non-Hamiltonian simplicial polyhedron by Branko Grünbaum in 1967. The Goldner–Harary graph is a planar graph:...

coloring is a property of a uniform figure (uniform tiling or uniform polyhedron) that is colored to be vertex-transitive. Different symmetries can be...

Topaz's crystal structure using polyhedrons showcasing the aluminum octahedron (grey), silica tetrahedron (blue), oxygen (red), and fluorine (green)....

List of Canadian exchange-traded funds dqd, an operation on polyhedrons in Conway polyhedron notation This disambiguation page lists articles associated...

three-dimensional motion of the surface of the polyhedron, cut to form a polyhedral net, from the polyhedron into a flat and non-self-overlapping placement...

vertices of the regular or quasi-regular polyhedron. Others share the same vertices and edges as other polyhedron. The grouping below exhibit some of these...

Reverse 10 francs 137 × 66 mm Red-brown Leonhard Euler; development of the polyhedron, the bridges of Königsberg Gamma function; table for the calculation of...

geometry, the octahemioctahedron or octatetrahedron is a nonconvex uniform polyhedron, indexed as U3. It contains twelve faces (eight triangles and four hexagons)...

parallelepiped are a hexahedron with three pairs of parallel faces, a polyhedron with six faces (hexahedron), each of which is a parallelogram, and a prism...

geometry, the nonconvex great rhombicosidodecahedron is a nonconvex uniform polyhedron, indexed as U67. It has 62 faces (20 triangles, 30 squares and 12 pentagrams)...

A tridecahedron, or triskaidecahedron, is a polyhedron with thirteen faces. There are numerous topologically distinct forms of a tridecahedron, for example...

other polyhedra, examples are some of the Johnson solids and Schönhardt polyhedron. It has a relationship with the honeycombs and polytopes. It can be found...

In geometry, the small triambic icosahedron is a star polyhedron composed of 20 intersecting non-regular hexagon faces. It has 60 edges and 32 vertices...

The dual polyhedron of the triangular orthobicupola is the trapezo-rhombic dodecahedron. It is a plesiohedron, a space-filling polyhedron defined by...

computational geometry, the problem of computing the intersection of a polyhedron with a line has important applications in computer graphics, optimization...

Star polyhedron – Polyhedron with some pattern of nonconvexity Kepler–Poinsot polyhedron – Any of 4 regular star polyhedra uniform star polyhedron – Self-intersecting...

analysis situs. Leonhard Euler's Seven Bridges of Königsberg problem and polyhedron formula are arguably the field's first theorems. The term topology was...

a polyhedron inscribed in a sphere, ellipsoid, or polyhedron) has each vertex on the outer figure; if the outer figure is a polygon or polyhedron, there...

of a regular polyhedron {p, q} is constrained by an inequality, related to the vertex figure's angle defect: 1 p + 1 q > 1 2 : Polyhedron (existing in...

In geometry, the excavated dodecahedron is a star polyhedron that looks like a dodecahedron with concave pentagonal pyramids in place of its faces. Its...

great snub disicosidisdodecahedron) is a degenerate nonconvex uniform polyhedron, indexed last as U75. It has 124 faces (40 triangles, 60 squares, and...

Diameter Circumference Disk Area Three-dimensional Surface area Volume Polyhedron Platonic Solid Tetrahedron Reuleaux cuboid Cube Octahedron Dodecahedron...

an abstract regular polyhedron, containing half the faces of a regular icosahedron. It can be realized as a projective polyhedron (a tessellation of the...

that differs significantly from an ellipsoid. It resembles an irregular polyhedron with several slightly concave facets and surface relief of up to 20 km...

face, and is therefore a polyhedron. Each face must join exactly two cells, analogous to the way in which each edge of a polyhedron joins just two faces....

using these shapes for this lower bound application. Like the Schönhardt polyhedron, these polyhedra have no triangulation into tetrahedra unless additional...

In geometry, a monogon is a curve, considered by some as a polygon with one edge and one vertex. It has Schläfli symbol {1}. In Euclidean geometry a monogon...

Polyhedron is a peer-reviewed scientific journal covering the field of inorganic chemistry. It was established in 1955 as the Journal of Inorganic and...

icosahedron, sometimes called Jessen's orthogonal icosahedron, is a non-convex polyhedron with the same numbers of vertices, edges, and faces as the regular icosahedron...

In convex geometry and polyhedral combinatorics, the extension complexity of a convex polytope P {\displaystyle P} is the smallest number of facets among...

an indexed list of the uniform and stellated polyhedra from the book Polyhedron Models, by Magnus Wenninger. The book was written as a guide book to building...

A triangular bipyramid is a hexahedron, a polyhedron with six triangular faces. It is constructed by attaching two tetrahedra face-to-face. The same shape...

for instructional or artistic purposes, including: Polyhedron model, a physical model of a polyhedron Mathematical Models (Cundy and Rollett), a book about...

polyhedra: the skeleton of a polyhedron forms a graph, the vertices of which are the vertices of the polyhedron, but polyhedron vertices have additional structure...

shape of a counterexample. Leonid Makar-Limanov later introduced a Newton polyhedron associated with a minimal counterexample, obtaining a sharper estimate...

compound of small stellated dodecahedron and great dodecahedron is a polyhedron compound where the great dodecahedron is internal to its dual, the small...

introduced the Goldberg polyhedron family, whose faces are pentagons and hexagons. The dual of such a polyhedron is geodesic polyhedron, described as an almost...

prism, a process known as elongation. The difference between these two polyhedrons is that one of the two square cupolas is twisted by 45 degrees, a process...

single chain of four silicon (Si) tetrahedrons [Si4O8(OH)4]∞ and sixfold polyhedrons of [NaO(OH)2(H2O)3] and [NaO(OH)(H2O)4] centered by sodium (Na). Pekov...

In geometry, the hexagonal prism is a prism with hexagonal base. this polyhedron has 8 faces, 18 edges, and 12 vertices. A hexagonal prism has twelve vertices...

In geometry, the augmented triangular prism is a polyhedron constructed by attaching an equilateral square pyramid onto one of the square faces of a triangular...

In geometry, a polyhedron is a solid in three dimensions with flat faces and straight edges. Every edge has exactly two faces, and every vertex is surrounded...

model of a convex polyhedron by connecting together rigid plates for each of the polyhedron faces with flexible hinges along the polyhedron edges, then this...

the boundary of a unique convex polyhedron, by Alexandrov's uniqueness theorem. In the case of a biscornu, this polyhedron is a flattened square antiprism...

sum of the numbers of vertices and faces minus the number of edges of a polyhedron that has no holes equals 2, a number now commonly known as the Euler characteristic...

In geometry, a skew apeirohedron is an infinite skew polyhedron consisting of nonplanar faces or nonplanar vertex figures, allowing the figure to extend...

In geometry, the gyrobifastigium is a polyhedron that is constructed by attaching a triangular prism to the square face of another one. It is an example...

surface of a polyhedron is called its development. The polyhedron can be thought of as being folded from a sheet of paper (a net for the polyhedron) and it...

The expanded icosidodecahedron is a polyhedron, constructed as an expanded icosidodecahedron. It has 122 faces: 20 triangles, 60 squares, 12 pentagons...

regular polyhedron, containing half the faces of a regular octahedron. It has 4 triangular faces, 6 edges, and 3 vertices. Its dual polyhedron is the hemicube...

geometry, the great complex icosidodecahedron is a degenerate uniform star polyhedron. It has 12 vertices, and 60 (doubled) edges, and 32 faces, 12 pentagrams...

relies on repetition of simple structures, similar to the faces of a polyhedron. Each face in turn is formed by a repetition of simpler sub-units, with...

all of its vertices off, a process known as truncation. The resulting polyhedron has 4 equilateral triangles and 4 regular hexagons, 18 edges, and 12 vertices...

Various refinements in the shape have been called choppers, discoids, polyhedrons, subspheroid, etc. To date no reasons for the variants have been ascertained:...

general any polyhedron (or polytope) can also be truncated with a degree of freedom as to how deep the cut is, as shown in Conway polyhedron notation truncation...

triangular faces. The triakis tetrahedron is a Catalan solid, the dual polyhedron of a truncated tetrahedron, an Archimedean solid with four hexagonal and...

lines, as well as the resulting interior points. Such shapes are called polyhedrons and include cubes as well as pyramids such as tetrahedrons. Other three-dimensional...

with "figures" so that the theorem applies to any pair of polygons or polyhedrons that are congruent. In a Euclidean system, congruence is fundamental;...

for some integer d ≥ 2. A characteristic polyhedron (also called an admissible polygon) of f is a polyhedron in Rd, having 2d vertices, such that in each...

A dihedron (pl. dihedra) is a type of polyhedron, made of two polygon faces which share the same set of n edges. In three-dimensional Euclidean space,...

the triacontahedron as it is the most common thirty-faced polyhedron, is a convex polyhedron with 30 rhombic faces. It has 60 edges and 32 vertices of...

Waterman projections from the W5 convex hull. To project the sphere to the polyhedron, the Earth is divided into eight octants. Each meridian is drawn as three...

In geometry, a near-miss Johnson solid is a convex polyhedron whose faces are close to being regular polygons but some or all of which are not precisely...

a uniform star polyhedron, indexed as U69. It is given a Schläfli symbol sr{5⁄3,3}, and Coxeter-Dynkin diagram . In the book Polyhedron Models by Magnus...

semi-regular and stellated polyhedra have been made. A cuboid is a rectilinear polyhedron. That is, all its edges form right angles. Or in other words (in the majority...

include: Line–plane intersection Line–sphere intersection Intersection of a polyhedron with a line Line segment intersection Intersection curve Determination...

twice. For instance, for any polyhedral graph, the faces of a convex polyhedron that represents the graph provide a cycle double cover of the graph: the...

The snub rhombicuboctahedron is a polyhedron, constructed as a truncated rhombicuboctahedron. It has 74 faces: 18 squares, and 56 triangles. It can also...

disease. Jakob Steininger and Sergey Yurkevich of Vienna describe a convex polyhedron without Rupert's property, which they call a 'noperthedron'. 29 August...

points are vertices of a polygon or polyhedron, the line segment is either an edge (of that polygon or polyhedron) if they are adjacent vertices, or a...

stellation pattern is a two-dimensional diagram in the plane of some face of a polyhedron, showing lines where other face planes intersect with this one. The lines...

faces are all regular, it is a semiregular polyhedron. A crossed hexagonal antiprism is a star polyhedron, topologically identical to the convex hexagonal...

removing parts of a polygon, polyhedron or polytope, without creating any new vertices. New edges of a faceted polyhedron may be created along face diagonals...

which are approximately 1.07 times as long as the other edges. This polyhedron has tetrahedral symmetry. Topologically, as a near-miss Johnson solid...

as Schwarz's boot, Schwarz's polyhedron, or the Chinese lantern. As Schwarz showed, for the surface area of a polyhedron to converge to the surface area...

In geometry, a zonohedron is a convex polyhedron that is centrally symmetric, every face of which is a polygon that is centrally symmetric (a zonogon)...

chromate(VI) species in acid medium and ab initio studies of these species". Polyhedron. 16 (21): 3835–3846. doi:10.1016/S0277-5387(97)00128-9. Holleman, Arnold...

geometry, most notably on Hilbert's third problem and the Sydler π/4 polyhedron. Sydler was born in 1921 in Neuchâtel, Switzerland. He graduated from...

anticube. If all its faces are regular, it is a semiregular polyhedron or uniform polyhedron. A nonuniform D4-symmetric variant is the cell of the noble...

polyhedron). Alternatively, an expression in terms of the face areas and surface normals may be derived using the divergence theorem (see Polyhedron §...

In geometry, the small rhombidodecahedron is a nonconvex uniform polyhedron, indexed as U39. It has 42 faces (30 squares and 12 decagons), 120 edges, and...

dodecahedron. The truncated great stellated dodecahedron is a degenerate polyhedron, with 20 triangular faces from the truncated vertices, and 12 (hidden)...

In geometry, the great stellated dodecahedron is a Kepler–Poinsot polyhedron, with Schläfli symbol {5⁄2, 3}. It is one of four nonconvex regular polyhedra...

Similarly, the group of symmetries of a polyhedron acts on the vertices, the edges, and the faces of the polyhedron. A group action on a vector space is...

diagram, that of a polyhedron, was described by Duncan Sommerville as follows: A very useful method of representing a convex polyhedron is by plane projection...

geometry, the tetrahemihexahedron or hemicuboctahedron is a uniform star polyhedron, indexed as U4. It has 7 faces (4 triangles and 3 squares), 12 edges,...

"Precinct 41 Major Crime Unit" 03:36 7. "The Insulindian Miracle" 02:24 8. "Polyhedrons" 03:09 9. "Live With Me" 02:40 10. "The Field Autopsy" 02:31 11. "Miss...

G2 Hn Regular polygon Triangle Square p-gon Hexagon Pentagon Uniform polyhedron Tetrahedron Octahedron • Cube Demicube Dodecahedron • Icosahedron Uniform...

whenever they are right pyramids and bipyramids. The Kleetope of a polyhedron is a new polyhedron made by replacing each face of the original with a pyramid,...

geometry, a space diagonal (also interior diagonal or body diagonal) of a polyhedron is a line connecting two vertices that are not on the same face. Space...

dodecicosidodecahedron (or small dodekicosidodecahedron) is a nonconvex uniform polyhedron, indexed as U33. It has 44 faces (20 triangles, 12 pentagons, and 12 decagons)...

the town to be destroyed, saving the miraculous Polyhedron. The Haruspex's ending destroys the Polyhedron to allow the production of a panacea, saving the...

octahedron is a faceting of the cube, meaning that it is a polyhedron or compound polyhedron within a cube that uses only the vertices of the cube. Faceting...

q. For example, {5⁄2} is a pentagram; {5⁄1} is a pentagon. A regular polyhedron that has q regular p-sided polygon faces around each vertex is represented...

surfaces is the Kleinian model. Dini's surface Hyperbolic 3-manifold Ideal polyhedron Mostow rigidity theorem Murakami–Yano formula Pseudosphere Grigor'yan...

elements. The 5-cube is 5th in a series of hypercube: The regular skew polyhedron {4,5| 4} can be realized within the 5-cube, with its 32 vertices, 80 edges...

convex polyhedron forms a 3-connected planar graph, and every 3-connected planar graph can be represented as the graph of a convex polyhedron. For this...

linear equalities and inequalities. Such a constraint set is called a polyhedron or a polytope if it is bounded. Second-order cone programming (SOCP) is...

definition coincides with the one that has been given above. A convex polyhedron is degenerate if either two adjacent facets are coplanar or two edges...

up to 1300 listeners a concert hall. The shape of the open, irregular, polyhedron glass building blends in with the old building. Most of the stately rooms...

A pseudo-uniform polyhedron is a polyhedron which has regular polygons as faces and has the same vertex configuration at all vertices but is not vertex-transitive:...

In geometry, the small cubicuboctahedron is a uniform star polyhedron, indexed as U13. It has 20 faces (8 triangles, 6 squares, and 6 octagons), 48 edges...

In geometry, a parallelohedron or Fedorov polyhedron is a convex polyhedron that can be translated without rotations to fill Euclidean space, producing...

thymol with dinuclear Cu(II)-2-phenyl propionate-bipyridine complex". Polyhedron. 266 117312. doi:10.1016/j.poly.2024.117312. Retrieved 22 February 2026...

In geometry, the Bilinski dodecahedron is a convex polyhedron with twelve congruent golden rhombus faces. It has the same topology as the face-transitive...

simple polyhedron is a three-dimensional polyhedron whose vertices are adjacent to three edges and three faces. The dual to a simple polyhedron is a simplicial...

In geometry, the augmented pentagonal prism is a polyhedron that can be constructed by attaching an equilateral square pyramid onto the square face of...

tile) three-dimensional space, including the cube (the only Platonic polyhedron to do so), the rhombic dodecahedron, the truncated octahedron, and triangular...

rhombhectotriadiohedron, rhombic 132-hedron, or equilateral dodecazonohedron is a polyhedron composed of 132 rhombic faces. Rhombic faces have five positions within...

can be time-consuming. A third criterion is based on a characteristic polyhedron. This criterion is used by a method called Characteristic Bisection. It...

92 faces while its dual polyhedron, the pentagonal hexecontahedron, has 92 vertices. On the other hand, as a simple polyhedron, the final stellation of...

perimeter. Consider a polyhedron that is topologically equivalent to a sphere, such as any convex polyhedron. Any vertex of the polyhedron will have several...

Diameter Circumference Disk Area Three-dimensional Surface area Volume Polyhedron Platonic Solid Tetrahedron Reuleaux cuboid Cube Octahedron Dodecahedron...

In geometry, the triakis truncated tetrahedron is a convex polyhedron made from 4 hexagons and 12 isosceles triangles. It can be used to tessellate three-dimensional...

machine, built by Proteus in the basement and consisting of a modular polyhedron. Proteus reveals to a reluctant Susan that the computer wants to conceive...

Diameter Circumference Disk Area Three-dimensional Surface area Volume Polyhedron Platonic Solid Tetrahedron Reuleaux cuboid Cube Octahedron Dodecahedron...

for the integrality of a polyhedron. Thus, the optimization of a linear objective over the integral points of such a polyhedron can be done using techniques...

quasiregular polyhedron is a uniform polyhedron which has just two kinds of face alternating around each vertex. A regular polyhedron is a uniform polyhedron which...

having internal angle ⁠2π/n⁠radians (⁠360/n⁠ degrees). For a regular polyhedron whose Schläfli symbol is {m, n}, the number of polygonal faces is : N...

dodecahemicosahedron (or small dodecahemiicosahedron) is a nonconvex uniform polyhedron, indexed as U65. It has 22 faces (12 pentagons and 10 hexagons), 60 edges...

{\displaystyle 25^{2}-23^{2}} . Skilling's figure, a degenerate uniform polyhedron, has Euler characteristic χ = − 96. {\displaystyle \chi =-96.} Every integer...

In geometry, the cubohemioctahedron is a nonconvex uniform polyhedron, indexed as U15. It has 10 faces (6 squares and 4 regular hexagons), 24 edges and...

and Victim of Deception. On May 29, they released a cover album titled Polyhedron, containing covers of songs by Do As Infinity, Joe Yellow, Hatsune Miku...

suspended shapes consist of five different types of regular, convex polyhedrons known as 'platonic solids'. The Constellation is lit at night. The whole...

Diameter Circumference Disk Area Three-dimensional Surface area Volume Polyhedron Platonic Solid Tetrahedron Reuleaux cuboid Cube Octahedron Dodecahedron...

isosceles triangle. In the Dorman Luke construction, each face of a dual polyhedron is the dual polygon of the corresponding vertex figure. As an example...

there are three types of inputs. They are simple polyhedron, geometrical polyhedron and multiple polyhedrons. Before defining the mesh type it is necessary...

Calculus Topology Leonard Euler Seven Bridges of Königsberg and Euler's polyhedron formula Trigonometry Hipparchus Constructed the first trigonometric table...

polyhedron can be seen as a trigonal trapezohedron.[citation needed] Kumar, C. P. Anil (2020). "On the Coherent Labelling Conjecture of a Polyhedron in...

astronomy, aeronomics, and solar physics. The spacecraft was a 26-sided polyhedron 1.4 metres (4.6 ft) in diameter. All faces (except the top and bottom)...

Does every convex polyhedron have Rupert's property? Shephard's problem (a.k.a. Dürer's conjecture) – does every convex polyhedron have a net, or simple...

two inches. Pommel shapes also vary, between classic spheres, various polyhedrons, arming sword-style disks, or most commonly teardrops or eggs. Bokken...

symmetry polyhedra with stretched or flattened hexagons, like these Goldberg polyhedron G(2,0): There are also 9 Johnson solids with regular hexagons: The debate...

In geometry, a trigonal trapezohedron is a polyhedron with six congruent quadrilateral faces, which may be scalene or rhomboid. The variety with rhombus-shaped...

n-antidipyramid, n-antibipyramid, n-deltohedron, or n-antitegum, is the dual polyhedron of an n-gonal antiprism. The 2n faces of an n-trapezohedron are congruent...

peak or (n−3)-face of the polyhedron Edge the ridge or (n−2)-face of the polyhedron Face the facet or (n−1)-face of the polyhedron Vertex the (n−4)-face of...

geometry, the heptagonal prism is a prism with heptagonal base. This polyhedron has 9 faces (2 bases and 7 sides), 21 edges, and 14 vertices. The area...

polynomial time? Can one find a simple closed quasigeodesic on a convex polyhedron in polynomial time? Can a simultaneous embedding with fixed edges for...

Diameter Circumference Disk Area Three-dimensional Surface area Volume Polyhedron Platonic Solid Tetrahedron Reuleaux cuboid Cube Octahedron Dodecahedron...

and the graph remains connected. Every 4-connected polyhedron can be realized as the ideal polyhedron, and the tetrakis hexahedron is such. Naturally occurring...

number. The geometrical pattern can be described as a polyhedron where the vertices of the polyhedron are the centres of the coordinating atoms in the ligands...

In geometry, the great snub icosidodecahedron is a nonconvex uniform polyhedron, indexed as U57. It has 92 faces (80 triangles and 12 pentagrams), 150...

Diameter Circumference Disk Area Three-dimensional Surface area Volume Polyhedron Platonic Solid Tetrahedron Reuleaux cuboid Cube Octahedron Dodecahedron...

and 120 edges. Johannes Kepler in Harmonices Mundi (1618) named this polyhedron a rhombicosidodecahedron, being short for truncated icosidodecahedral...

is called a torus. The term toroid is also used to describe a toroidal polyhedron. In this context a toroid need not be circular and may have any number...

(1991). "Characterization of aluminum isopropoxide and aluminosiloxanes". Polyhedron. 10 (14): 1639–46. doi:10.1016/S0277-5387(00)83775-4. Turova, N. Y.; Kozunov...

or hexahedrons) or sexahedron (pl.: sexahedra or sexahedrons) is any polyhedron with six faces. A cube, for example, is a regular hexahedron with all...

because of its degeneracy in the Euclidean case. A digon as a face of a polyhedron is degenerate because it is a degenerate polygon, but sometimes it can...

Diameter Circumference Disk Area Three-dimensional Surface area Volume Polyhedron Platonic Solid Tetrahedron Reuleaux cuboid Cube Octahedron Dodecahedron...

has only one unstable point of balance (the previously known monostatic polyhedron does not qualify, as it has several unstable equilibria). A sphere weighted...

Bis(2-ethylhexyl) phthalate, a PVC plasticizer Discrete oriented polytope or polyhedron in computer graphics DSD over PCM, a protocol for Direct Stream Digital...

system of divisors of dimension 2 Net (polyhedron), an arrangement of polygons that can be folded up to form a polyhedron An incidence structure consisting...

electron count. Closo- represents a complete polyhedron, while nido-, arachno- and hypho- stand for polyhedrons that are missing one, two and three vertices...

The compound of five octahedra is one of the five regular polyhedron compounds, and can also be seen as a stellation. It was first described by Edmund...

two regular dodecagon caps. If faces are all regular, it is a uniform polyhedron. It is used in the construction of two prismatic uniform honeycombs: The...

facet of a polyhedron any polygon whose corners are vertices of the polyhedron, including polygons that are not faces. To facet a polyhedron is to find...

ashlar with copper gnomons. It is a multi-faceted sundial made out of a polyhedron. It indicates the time in the following cities around the world: Amsterdam...

isotoxal polyhedron is also an isotoxal polyhedron. (See the Dual polyhedron article.) The dual of a convex polyhedron is also a convex polyhedron. There...

polyhedral combinatorics, the Kleetope of a polyhedron or higher-dimensional convex polytope P is another polyhedron or polytope PK formed by replacing each...

office (CO) Cofunction, or Co, in trigonometry Cuboctahedron, a uniform polyhedron Nguyễn Hữu Có (1925–2012), Vietnamese general Conrado Co (born 1940),...

Diameter Circumference Disk Area Three-dimensional Surface area Volume Polyhedron Platonic Solid Tetrahedron Reuleaux cuboid Cube Octahedron Dodecahedron...

general number of dimensions. A polygon is a polytope in two dimensions, a polyhedron in three dimensions, and so on in higher dimensions (such as a 4-polytope...

the basic unit for these foams, but the most representative shape is a polyhedron with 13 faces. Cell size and cell size distribution are critical parameters...

Petrie polygon Skew quadrilateral Regular skew polyhedron Skew apeirohedron (infinite skew polyhedron) Skew lines Coxeter 1973, §1.1 Regular polygons;...

faces. This polyhedron can be constructed by truncating two opposite vertices of a cube, of a trigonal trapezohedron (a convex polyhedron with six congruent...

This picture clarifies the relationship between a polyhedron's side length, its surface area, and its volume....

in Islamic architecture Smoothed octagon Wenninger, Magnus J. (1974), Polyhedron Models, Cambridge University Press, p. 9, ISBN 9780521098595. Dao Thanh...

no definite end to Invisible Cities because "this book was made as a polyhedron, and it has conclusions everywhere, written along all of its edges." Over...

displace can be added to a plane to simulate a hilly terrain. Geosphere: Produces spheres and hemispheres based on three classes of regular polyhedrons....

G2 Hn Regular polygon Triangle Square p-gon Hexagon Pentagon Uniform polyhedron Tetrahedron Octahedron • Cube Demicube Dodecahedron • Icosahedron Uniform...

A pentagonal bipyramid or pentagonal dipyramid is a polyhedron with ten triangular faces. It is constructed by attaching two pentagonal pyramids to each...

In geometry, an edge-contracted icosahedron is a polyhedron with 18 triangular faces, 27 edges, and 11 vertices. It can be constructed from the regular...

(2006). "The Crystal Structure of Tetrakis(dimethylamino)titanium(IV)". Polyhedron. 25 (4): 923–929. doi:10.1016/j.poly.2005.10.019. Creaser, C. S.; Creighton...

The expanded cuboctahedron is a polyhedron constructed by expansion of the cuboctahedron. It has 50 faces: 8 triangles, 30 squares, and 12 rhombs. The...

to determine whether one polyhedron can be cut into pieces and reassembled ("dissected") into another, and whether a polyhedron or its dissections can tile...

In geometry, an icositetrahedron refers to a polyhedron with 24 faces, none of which are regular polyhedra. However, many are composed of regular polygons...

geometry. For the metric space of surface distances on a convex polyhedron, cutting the polyhedron along the cut locus produces a shape that can be unfolded...

Decagonal prism Hendecagonal prism Dodecagonal prism ... Apeirogonal prism Polyhedron image ... Spherical tiling image Plane tiling image Vertex config. 2.4...

icosidodecahedron has rectangles instead of squares. This nonuniform polyhedron is topologically equivalent to the Archimedean solid. Alternate interchangeable...

edge lengths. Similarly, if a polyhedron is cut along an edge, the corresponding angle is cut into two. Cutting a polyhedron typically also introduces new...

Trigonal trapezohedron Regular skew polyhedron Waterman polyhedron Wedge Polyhedral compound and Uniform polyhedron compound Compound of cube and octahedron...

known for his work involving folding paper, origami tessellations and 3D polyhedrons. Resch studied art at the University of Iowa receiving his Master of...

as truncated small rhombicuboctahedron or beveled cuboctahedron—is a polyhedron, constructed from a rhombicuboctahedron by truncating its vertices. It...

pyramids can be found as components of many polyhedrons. Attaching its base to the pentagonal face of another polyhedron is an example of the construction process...

polyhedra with six quadrilateral faces. A rectangular cuboid is a convex polyhedron with six rectangle faces. The dihedral angles of a rectangular cuboid...

polyhedron is one example of a toroidal polyhedron with this property. The Szilassi polyhedron's dual, the Császár polyhedron, is the only polyhedron...

Diameter Circumference Disk Area Three-dimensional Surface area Volume Polyhedron Platonic Solid Tetrahedron Reuleaux cuboid Cube Octahedron Dodecahedron...

Exchange in Copper(II) Halide Dimers: (4,4′-Bipyridinium)Cu2Cl6−x BRX". Polyhedron. 25 (10): 2093–2100. doi:10.1016/j.poly.2006.01.005. Hasselgren, Catrin;...

line of action as described in planar screw theory. Dual polygon Dual polyhedron Polar curve Brokard's theorem Johnson RA (1960). Advanced Euclidean Geometry:...

anions, and each cation is surrounded by coordinated anions which form a polyhedron. Ions assemble into a crystal lattice when the lattice energy released...

polyhedron are extended indefinitely the space around the polyhedron is divided into unbounded sub spaces and often a number of bounded polyhedrons or...

a stacked polytope. In three dimensions, every stacked polytope is a polyhedron with triangular faces, and several of the deltahedra (polyhedra with equilateral...

A polycube is an orthogonal polyhedron formed by joining one or more equal cubes face to face. Polycubes are the three-dimensional analogues of the planar...

Diameter Circumference Disk Area Three-dimensional Surface area Volume Polyhedron Platonic Solid Tetrahedron Reuleaux cuboid Cube Octahedron Dodecahedron...

the hyperplanes. A hyperplane H is called a "support" hyperplane of the polyhedron P if P is contained in one of the two closed half-spaces bounded by H...

In geometry, an enneahedron (or nonahedron) is a polyhedron with nine faces. There are 2606 types of convex enneahedra, each having a different pattern...

geometry, the nonconvex great rhombicuboctahedron is a nonconvex uniform polyhedron, indexed as U17. It has 26 faces (8 triangles and 18 squares), 48 edges...

Easter Eggs show David X. Cohen displaying a collection of different Polyhedrons, and extra outtakes of Billy West. The Blu-ray also exclusively features...

solid-state NMR and 127I NQR as probes to elucidate the composition of "GaI"". Polyhedron. 35 (1): 96–100. doi:10.1016/j.poly.2012.01.003. ISSN 0277-5387. Ge(−1)...

compact hyperbolic Coxeter polytopes that are bounded by a fundamental polyhedron, and the highest dimension that holds arithmetic discrete groups of reflections...

G2 Hn Regular polygon Triangle Square p-gon Hexagon Pentagon Uniform polyhedron Tetrahedron Octahedron • Cube Demicube Dodecahedron • Icosahedron Uniform...

technology Uranium carbide, a hard refractive ceramic material Uniform polyhedron compound, a type of geometry Universal Column, a type of H-beam Folding...

edge set of a triangle, K4 a tetrahedron, etc. The Császár polyhedron, a nonconvex polyhedron with the topology of a torus, has the complete graph K7 as...

degenerate polyhedron. An angle of 180° means the faces are parallel, as in a tiling. An angle greater than 180° exists on concave portions of a polyhedron. Every...

In geometry, a pentakis dodecahedron or kisdodecahedron is a polyhedron created by attaching a pentagonal pyramid to each face of a regular dodecahedron;...

[FeI3(AsMe3)2], from the reaction of Me3AsI2 with unactivated iron powder". Polyhedron. 55: 67–72. doi:10.1016/j.poly.2013.02.066. Greenwood & Earnshaw 1997...

scenario "has to be good". Games Review (Volume 2, Issue 3 - Dec 1989) Polyhedron (Issue 49 - Vol. 9, No. 5) Knights of the Dinner Table Magazine (Issue...

parallelohedron identified by Evgraf Fedorov. In other words, it is a space-filling polyhedron, meaning the elongated dodecahedron and its copy can tile space face-to-face...

In geometry, the snub disphenoid is a convex polyhedron with 12 equilateral triangles as its faces. It is an example of deltahedron and Johnson solid....

coincidence: every convex polyhedron can be turned into a connected, simple, planar graph by using the Schlegel diagram of the polyhedron, a perspective projection...

and 1 solid: 8 + 12 + 6 + 1 = 27 = 33. Another three-dimensional convex polyhedron, the regular octahedron, is also centrally symmetric, and has 6 vertices...

In geometry, a hendecagrammic prism is a star polyhedron made from two identical regular hendecagrams connected by squares. The related hendecagrammic...

G2 Hn Regular polygon Triangle Square p-gon Hexagon Pentagon Uniform polyhedron Tetrahedron Octahedron • Cube Demicube Dodecahedron • Icosahedron Uniform...

year earlier by Thomas Kirkman, who, in particular, gave an example of a polyhedron without Hamiltonian cycles. Even earlier, Hamiltonian cycles and paths...

spheroids dating to 429 ka can be quantitatively distinguished from polyhedrons and exhausted cores, showing strong evidence that some were deliberately...

on the other hand, has twenty vertices, likewise the most a regular polyhedron can have. This is because the icosahedron and dodecahedron are duals of...

dyes Gadolinium-based MRI contrast agent Great dodecahedron, a regular polyhedron gad, ISO 639-3 code for the Gaddang language, spoken in the Philippines...

thymol with dinuclear Cu(II)-2-phenyl propionate-bipyridine complex". Polyhedron. 266 117312. doi:10.1016/j.poly.2024.117312. Retrieved 22 February 2026...

a system of notation dedicated to describing polyhedra called Conway polyhedron notation. In the theory of tessellations, he devised the Conway criterion...

be similarly embedded into the 10-demicube. Skew polygon Infinite skew polyhedron McMullen, Peter; Schulte, Egon (2002). Abstract Regular Polytopes. Encyclopedia...

\mathbf {X} } assigned to a particular site j {\displaystyle j} is a convex polyhedron. The resulting configuration is called a power diagram. Assume the particular...

the edges of the other length form an equatorial zigzag path around the polyhedron. They are the dual polyhedra of the uniform antiprisms. A commonly seen...

In geometry, a plesiohedron is a special kind of space-filling polyhedron, defined as the Voronoi cell of a symmetric Delone set. Three-dimensional Euclidean...

coordinates, a coordinate system using a simplex or tetrahedron as its basis polyhedron. The four basis (but not necessarily unit) vectors stem from the center...

In geometry, the dodecadodecahedron is a nonconvex uniform polyhedron, indexed as U36. It is the rectification of the great dodecahedron (and that of its...

triacontahedron has the most faces of any other strictly convex polyhedron where every face of the polyhedron has the same shape. Projected into a sphere, the edges...

Diameter Circumference Disk Area Three-dimensional Surface area Volume Polyhedron Platonic Solid Tetrahedron Reuleaux cuboid Cube Octahedron Dodecahedron...

River Water: Assessment of Plants, Intermittent Artificial Aeration and Polyhedron Hollow Polypropylene Balls. Water, Air and Soil Pollution, 197 (1-4),...

G2 Hn Regular polygon Triangle Square p-gon Hexagon Pentagon Uniform polyhedron Tetrahedron Octahedron • Cube Demicube Dodecahedron • Icosahedron Uniform...

model The triheptagonal tiling can be seen in a sequence of quasiregular polyhedrons and tilings: From a Wythoff construction there are eight hyperbolic uniform...

hyperbolic space that resembles a polyhedron in the sense that it has flat faces that meet along edges. Unlike a polyhedron, a pleated surface has no corners...

characteristic, classically the number of vertices minus edges plus faces of a polyhedron. Euler number (3-manifold topology) – see Seifert fiber space Lucky numbers...

the thirteen solids in 1865. In general, each face of a dual uniform polyhedron (including the Catalan solid) can be constructed by using the Dorman Luke...

Equal-area Jarke J. van Wijk Projects the globe onto a myriahedron: a polyhedron with a very large number of faces. 1909 Craig retroazimuthal = Mecca Retroazimuthal...

spot, and they produced several different types, including choppers, polyhedrons, and discoids. Nonetheless, specific shapes were likely not thought of...

uniformity when changing a spherical polyhedron to its planar counterpart can push faces through the centre of the polyhedron and back out the other side, changing...

mathematician known for his 1928 discovery of the Schönhardt polyhedron, a non-convex polyhedron that cannot be partitioned into tetrahedra without introducing...

and non-regular, the dyakis dodecahedron is a non-uniform polyhedron, a type of polyhedron that is not vertex-transitive and does not have regular polygon...

curve Concave polygon – Simple polygon which is not convex Convex polyhedron – Polyhedron that is the boundary of a convex set Convex polytope – Convex hull...

(the dual of the icosahedron) and the rhombic triacontahedron. Every polyhedron with icosahedral symmetry has 60 rotational (or orientation-preserving)...

Jean Rabe, ed. (July 1993). "The Gaming Is Hot at Winter Fantasy™". Polyhedron. Vol. 15, no. 7. Back Cover [p. 32 of scanned version]. "Ravenloft Creator...

limit set is ergodic. Ahlfors, Lars V. (February 1966). "Fundamental polyhedrons and limit point sets of Kleinian groups". Proceedings of the National...

Element Polyhedron Number of Faces Number of Triangles Fire Tetrahedron (Animation) 4 24 Air Octahedron (Animation) 8 48 Water Icosahedron (Animation)...

of students who debate the proof of the Euler characteristic for the polyhedron. Owen Barfield Barfield's Worlds is a dialogue in the Socratic tradition...

icosicosidodecahedron, or retroholosnub icosahedron) is a nonconvex uniform polyhedron, indexed as U72. It has 112 faces (100 triangles and 12 pentagrams), 180...

1992-2009 Israeli 5 new shekel Dodecagonal number Dodecahedron – any polyhedron with 12 faces. Dodecagram "Wolfram Demonstrations Project". demonstrations...

convex polytope, and the word "polyhedron" for the more general, possibly unbounded object (an n-dimensional polyhedron). Others (including this article)...

which is also the angle between Plateau borders: 109.471°. It is the dual polyhedron to the rectified truncated icosahedron, a near-miss Johnson solid. On the...

Euclidean reflection groups; for example, the symmetry group of each regular polyhedron is a finite Coxeter group. However, not all Coxeter groups are finite...

1432-1807/e, full text Richeson, David S. (23 July 2019). Euler's gem: the polyhedron formula and the birth of topology (New Princeton science library ed.)...

cuboctahedron form a polyhedron topologically equivalent to the snub cube; the other 24 form its mirror-image. The resulting polyhedron is vertex-transitive...

in non-associative algebras, for example alternative algebras Flexible polyhedron Flexible single master operation "Flexible", a song by Depeche Mode Flexible...

fields. Beck, Hosten & Schymura (2019) modelled the conjecture through a polyhedron, which is defined as follows: for a positive vector n {\displaystyle \mathbf...

theorem according to which the angular defects of the vertices of a convex polyhedron (the amount by which the angles at that vertex fall short of the 2 π {\displaystyle...

different shapes, wrapped in corn husks. These include those folded into polyhedrons called corundas and can vary in name if the filling is different. In...

square, inverted as {4/3}, is an octagram, t{4/3}={8/3}. The uniform star polyhedron stellated truncated hexahedron, t'{4,3}=t{4/3,3} has octagram faces constructed...

The pentagonal rotunda is a convex polyhedron with regular polygonal faces. These faces comprise ten equilateral triangles, six regular pentagons, and...

Retrieved 2024-04-20 – via Newspapers.com. "Convention Wrapup 1981". Polyhedron. Vol. 1, no. 3. Winter 1981–1982. p. 22. Retrieved 2024-04-20 – via Internet...

In geometry, a pentahedron (pl.: pentahedra) is a polyhedron with five faces or sides. There are no face-transitive polyhedra with five sides, and there...

The sculptures, painted by Molly Dilworth, consist of painted metal polyhedrons. The piece sits at roughly 50 feet wide and 12 feet tall and is mounted...

circles). The result can also be extended to quasigeodesics on a convex polyhedron, and to closed geodesics of reversible Finsler 2-spheres. The theorem...

(geometry) of a polygon (two-dimensional shape) Face (geometry) of a polyhedron (three-dimensional shape) Side, Turkey, a city in Turkey Side (Ainis)...

G2 Hn Regular polygon Triangle Square p-gon Hexagon Pentagon Uniform polyhedron Tetrahedron Octahedron • Cube Demicube Dodecahedron • Icosahedron Uniform...

the polyhedron by creating an imaginary sphere around each vertex, and painting it with various points and lines representing how the polyhedron divides...

quantities e-folding, exponential growth or decay Polygon folding, or polyhedron folding HD 109246 b or Fold, an exoplanet Amicus Therapeutics, NASDAQ...

corner of rock Anhedral (disambiguation) Euhedral, a crystal structure Polyhedron, a geometric shape This disambiguation page lists articles associated...

geometry, a vertex configuration is a shorthand notation for representing a polyhedron or tiling as the sequence of faces around a vertex. It has variously been...

In geometry, the compound of three cubes is a uniform polyhedron compound formed from three cubes arranged with octahedral symmetry. It has been depicted...

multi-part sculpture with two other bronze "magic stones" (eight-sided polyhedrons) and three "figures" (vertical abstract sculptures). One of these other...

submersion Regular polygons, polygons with all sides and angles equal Regular polyhedron, a generalization of a regular polygon to higher dimensions Regular polytope...

Diameter Circumference Disk Area Three-dimensional Surface area Volume Polyhedron Platonic Solid Tetrahedron Reuleaux cuboid Cube Octahedron Dodecahedron...

charts of financially traded assets Flag (geometry), part of a polygon, polyhedron or higher polytope Flag (linear algebra), an increasing sequence of subspaces...

the first stellation of the rhombic dodecahedron is a self-intersecting polyhedron with 12 faces, each of which is a non-convex hexagon. It is a stellation...

Diameter Circumference Disk Area Three-dimensional Surface area Volume Polyhedron Platonic Solid Tetrahedron Reuleaux cuboid Cube Octahedron Dodecahedron...

Atlanticus Cahill–Keyes projection Waterman butterfly projection Waterman polyhedron Major, Richard Henry (1865). Memoir on a mappemonde by Leonardo da Vinci...

Diameter Circumference Disk Area Three-dimensional Surface area Volume Polyhedron Platonic Solid Tetrahedron Reuleaux cuboid Cube Octahedron Dodecahedron...

(3-dimensional) represented using a variety of strategies, such as a polyhedron consisting of connected polygon faces. The software is expected to use...

Honeycomb made from unique polyhedrons...

imidazolium-based ionic liquids with tetrachloronickelate(II) anions". Polyhedron. 28 (12): 2355–2358. doi:10.1016/j.poly.2009.04.037. Cotton, F. A.; Faut...

polyhedra that tile space. Its edges lie on diagonals of the regular skew polyhedron, a surface with six squares meeting at each integer point of space. Several...

construct a regular polyhedron is via a fold-out net. To obtain a fold-out net of a polyhedron, one takes the surface of the polyhedron and cuts it along...

icosidodecahedron or stellatruncated icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U68. It has 62 faces (30 squares, 20 hexagons, and 12 decagrams)...

W88 or W-88 may also refer to: Great icosicosidodecahedron, a 52-faced polyhedron Stapac Jakarta, an Indonesian basketball club Air Harbor Airport in Greensboro...

G2 Hn Regular polygon Triangle Square p-gon Hexagon Pentagon Uniform polyhedron Tetrahedron Octahedron • Cube Demicube Dodecahedron • Icosahedron Uniform...

triangle Lenart sphere Schwarz triangle Spherical geometry Spherical polyhedron Triangulation (surveying) Todhunter, Isaac (1886). Spherical Trigonometry...

thiocyanogen, S2(CN)2, selenocyanogen, Se2(CN)2, and related compounds". Polyhedron. 19 (6): 681–688. doi:10.1016/S0277-5387(00)00304-1. Bossmann, Stefan...

truncated icosahedron is a convex polyhedron constructed as an augmented truncated icosahedron. It is a geodesic polyhedron {3,5+}3,0, with pentavalent vertices...

In geometry, the gyroelongated square bipyramid is a polyhedron with 16 triangular faces. it can be constructed from a square antiprism by attaching two...

point of the polyhedron induced by B x ≤ b {\displaystyle Bx\leq b} . This is because every point of a non-empty, bounded convex polyhedron can be represented...

In geometry, a prismatoid is a convex polyhedron whose vertices all lie in two parallel planes. Its lateral faces can be trapezoids or triangles. If both...

dodecahemicosahedron (or great dodecahemiicosahedron) is a nonconvex uniform polyhedron, indexed as U62. It has 22 faces (12 pentagrams and 10 hexagons), 60 edges...

complexity or vertex complexity) of the polyhedron: An oracle for WNEMPT, for a full-dimensional polyhedron P with a bound on its representation complexity...

antiparallelograms as their vertex figures, the cross-sections formed by slicing the polyhedron by a plane that passes near a vertex, perpendicularly to the axis between...

G2 Hn Regular polygon Triangle Square p-gon Hexagon Pentagon Uniform polyhedron Tetrahedron Octahedron • Cube Demicube Dodecahedron • Icosahedron Uniform...

and a rotation. A cube has the same set of symmetries, since it is the polyhedron that is dual to an octahedron. The group of orientation-preserving symmetries...

the vertices of an inscribed cantellated tesseract. The regular skew polyhedron, {4,8|3}, exists in 4-space with 8 square around each vertex, in a zig-zagging...

The triaugmented triangular prism, in geometry, is a convex polyhedron with 14 equilateral triangles as its faces. It can be constructed from a triangular...

lithic technology" An Early Stone Age in Western Africa? Spheroids and polyhedrons at Ounjougou, Mali". Journal of Lithic Studies. 4 (1). doi:10.2218/jls...

Geometric and Biological Modeling, (PDF) Bruce Baumgart, Winged-Edge Polyhedron Representation for Computer Vision. National Computer Conference, May...

(Nürnberg, (Germany): Bauer und Raspe, 1847), presented a proof of Euler's polyhedron theorem which relies on trees on pages 20–21. Also in 1847, the German...

of 1.48 and 1.37 Å, respectively. Each Ca2+ cation is surrounded by a polyhedron of eight oxygen atoms. The average distance between calcium and oxygen...

In geometry, the elongated triangular cupola is a polyhedron constructed from a hexagonal prism by attaching a triangular cupola. It is an example of a...

In geometry, an n-gonal truncated trapezohedron is a polyhedron formed by a n-gonal trapezohedron with n-gonal pyramids truncated from its two polar axis...

dodecacontachoron), coining the term polychoron being a 4D analogy to the 3D polyhedron, and 2D polygon, expressed from the Greek roots poly ("many") and choros...

Wiktionary, the free dictionary. Orthogonal ligand-protein pair Orthogonal polyhedron Up tack "perpendicular". Merriam-Webster.com Dictionary. Merriam-Webster...

polygon must have at least four vertices; there are no skew triangles. A polyhedron that has positive volume has vertices that are not all coplanar. Collinearity...

constructed by cutting off all the vertices of a cube. The resulting polyhedron has six octagons and eight triangles, having in total fourteen regular...

Dec 1990) Portal (Issue 7 - Oct 2000) Casus Belli (Issue 69 - May 1992) Polyhedron #75 Collette, Don (February 1992). "Capsule Reviews". White Wolf Magazine...

with a peripheral edge. Polyhedral tools are edged in the shape of a polyhedron. In addition there are spheroidal hammer stones. Light-duty tools are...

helix, tangent indicatrix of a curve of constant precession Spherical polyhedron Sphericity Tennis ball theorem Volume-equivalent radius Zoll sphere r...

spherical grid systems, HEALPix is not based on mapping a sphere to a polyhedron. In particular, the standard H=4, K=3 HEALPix projection has 12 quatrilateral...

pentagons 1 decagon Edges 105 Vertices 55 Vertex configuration 10(4.5.10) 3×5+3×10(3.4.5.4) Symmetry group C5v Dual polyhedron - Properties convex Net...

triangular prisms alongside two tetrahedra as cells. The complex Hessian polyhedron in C 3 {\displaystyle \mathbb {C} ^{3}} contains 72 regular complex triangular...

smallest convex polyhedron that contains all of these points. The blue lines together with the coordinate axes define the polyhedron of the LP relaxation...

published in Polyhedron #28 R6 Bigby's Tomb 5–7 Frank Mentzer 1984 Run at an unknown tournament in 1984, later published in Polyhedron #20 as "The 384th...

"Incursion" storyline running through July 2003's Dragon #309 and Dungeon #100/Polyhedron #159 focused on the githyanki heavily. Paizo Publishing, which held the...

In geometry, this polyhedron can be seen as either a polyhedral stellation or a compound. It can be seen as the compound of an icosahedron and dodecahedron...

is the undirected graph formed from the vertices and edges of a convex polyhedron. Alternatively, in purely graph-theoretic terms, the polyhedral graphs...

geometry, a rhombic enneacontahedron (plural: rhombic enneacontahedra) is a polyhedron composed of 90 rhombic faces; with three, five, or six rhombi meeting...

In geometry, the ten-of-diamonds decahedron is a space-filling polyhedron with 10 faces, 2 opposite rhombi with orthogonal major axes, connected by 8 identical...

geodesic spheres. They are composed of a framework of triangles in a polyhedron pattern. The structures are named for geodesics and are based upon geometric...

convex polyhedron that has the given graph as its vertices and edges and that has a midsphere, a sphere tangent to all of the edges of the polyhedron. Each...

octakaidecahedron) is a polyhedron with 18 faces. No octadecahedron is regular; hence, the name does not commonly refer to one specific polyhedron. In chemistry...

For polyhedra, an expanded polyhedron has all the faces of the original polyhedron, all the faces of the dual polyhedron, and new square faces in place...

bellows or an enema syringe (clyster). On the low wall behind the large polyhedron is a brazier with a goldsmith's crucible and a pair of tongs. To the left...

This uniform polyhedron compound is a composition of 5 small cubicuboctahedra, in the same vertex arrangement as the compound of 5 small rhombicuboctahedra...

(pinnacolo), that may be one of many designs: disk, ball, cone, bowl, polyhedron, or a combination thereof, that is supposed to be the signature of the...

triangles 20 squares 2 pentagons Edges 60 Vertices 30 Vertex configuration 20(3.43) 10(3.4.5.4) Symmetry group D5d Dual polyhedron - Properties convex Net...

( E {\displaystyle E} ) and faces ( F {\displaystyle F} ) of a convex polyhedron, and hence of a planar graph. The study and generalization of this formula...

faces, 20 edges and 10 vertices. This polyhedron is identified with the indexed name U79 as a uniform polyhedron. Note that the pentagram face has an ambiguous...

mirror removal and ratios of Coxeter group orders. The regular complex polyhedron 3{3}3{4}2, , in C 2 {\displaystyle \mathbb {C} ^{2}} has a real representation...

any problem, the convex hull of the solutions is an integral polyhedron; if this polyhedron has a nice/compact description, then we can efficiently find...

icosidodecahedron (or small ditrigonary icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U30. It has 32 faces (20 triangles and 12 pentagrams), 60...

Doo: A subdivision algorithm for smoothing down irregularly shaped polyhedrons, Proceedings on Interactive Techniques in Computer Aided Design, pp....

In geometry, a snub is an operation applied to a polyhedron. The term originates from Kepler's names of two Archimedean solids, for the snub cube (cubus...

motion of a net of a polyhedron from its flat unfolded state to the folded polyhedron, or vice versa. Although every convex polyhedron has a net with a blooming...

characters. Go for it!" Terra Traveller Times (Number 34 - May 1991) Polyhedron #70 Mixson, Allen (February 1992). "Capsule Reviews". White Wolf Magazine...

The GC construction can be thought of as subdividing the faces of a polyhedron with a lattice of triangular, square, or hexagonal polygons, possibly...

Apart from the heptagonal prism and heptagonal antiprism, no convex polyhedron made entirely out of regular polygons contains a heptagon as a face. Two...

geometry, an alternation or partial truncation is an operation on a polygon, polyhedron, tiling, or higher dimensional polytope that removes alternate vertices...

The biaugmented triangular prism is a polyhedron constructed from a triangular prism by attaching two equilateral square pyramids onto two of its square...

The dual polyhedron of any of these polyhedra may be formed as the convex hull of the center points of each face of the primal polyhedron, so the vertices...

convex polyhedron if and only if it is polyhedral. A three-dimensional polyhedron has a cubic graph if and only if it is a simple polyhedron. And, a...

sign of: (0, 2+√2, 2+√2, 2+2√2) (1, 1+√2, 1+√2, 3+2√2) The regular skew polyhedron, {8,4|3}, exists in 4-space with 4 octagonal around each vertex, in a...

subdivisions can be used to attain arbitrarily fine triangulations of a given polyhedron. An important open problem asks whether any two simplicial complexes with...

pentagonal orthobirotunda is one of the Johnson solids (J42). Its Conway polyhedron notation is at5jP5. As the name suggests, it can be constructed by elongating...

oxide)pyridine (OPPh2py). Molecular structure of Fe(NO3)2Cl(OPPh2py) · CH2Cl2". Polyhedron. 14 (9): 1229–1234. doi:10.1016/0277-5387(94)00372-L. Wah, Henri Li Kam;...

Diameter Circumference Disk Area Three-dimensional Surface area Volume Polyhedron Platonic Solid Tetrahedron Reuleaux cuboid Cube Octahedron Dodecahedron...

geometry, the gyroelongated pentagonal rotunda is a Johnson solid, a convex polyhedron with thirty equilateral triangles, six regular pentagons, and one regular...

Rupert property: a copy of the polyhedron, of the same or larger size, can be passed through a hole in the polyhedron. It was unknown whether this was...

polyhedron with octahedral symmetry: Klein modeled the quartic by a shape with octahedral symmetries and with points at infinity (an "open polyhedron")...

approach the preserved monotonicity trait is the line L. A three-dimensional polyhedron is called weakly monotonic in direction L if all cross-sections orthogonal...

or a tetragonal hexacontahedron) is a Catalan solid which is the dual polyhedron of the rhombicosidodecahedron, an Archimedean solid. It is one of six...

David F.; Wood, Robert J. (July 18, 2018). "Rotary-actuated folding polyhedrons for midwater investigation of delicate marine organisms". Science Robotics...

(out of 40,000) to be found under this radical. In Taoist cosmology, 龜 (Polyhedron) is the nature component of the Ba gua diagram 坎 Kǎn. Shang Oracle bone...

or more precisely an order-8 truncated triakis octahedron, is a convex polyhedron with 30 faces: 8 sets of 3 pentagons arranged in an octahedral arrangement...

via Internet Archive. "Dragon Magazine # 208" – via Internet Archive. "Polyhedron 105 : Free Download, Borrow, and Streaming : Internet Archive". "Dungeon...