Pseudo-polyomino

A pseudo-polyomino, also called a polyking, polyplet or hinged polyomino, is a plane geometric figure formed by joining one or more equal squares edge-to-edge or corner-to-corner at 90°. It is a polyform with square cells. The polyominoes are a subset of the polykings.

The name "polyking" refers to the king in chess. The n-kings are the n-square shapes which could be occupied by a king on an infinite chessboard in the course of legal moves.

Golomb uses the term pseudo-polyomino referring to kingwise-connected sets of squares.^[1]

There are three common ways of distinguishing polyominoes and polykings for enumeration:^[1]

• free polykings are distinct when none is a rigid transformation (translation, rotation, reflection or glide reflection) of another (pieces that can be picked up and flipped over).
• one-sided polykings are distinct when none is a translation or rotation of another (pieces that cannot be flipped over).
• fixed polykings are distinct when none is a translation of another (pieces that can be neither flipped nor rotated).

The following table shows the numbers of polykings of various types with n cells.

• Weisstein, Eric W. "Polyplet". MathWorld.