Girish Mahajan (Editor)

Polyking

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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.

Free, one-sided, and fixed polykings

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

  • 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.

    References

    Polyking Wikipedia
    (Text) CC BY-SA


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