7x7 constructed with the 94 pseudo-pentominoes, or pentaplets
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. ==Notes==