Polyking

A polyking (or 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 term pseudo-polyomino referring to kingwise-connected sets of squares.

Enumeration of polykings

Free, one-sided, and fixed polykings

There are three common ways of distinguishing polyominoes and polykings for enumeration: