Polyominoids may be generalized to other dimensions. An (n,k)-polyominoid is a set of k-dimensional cells in the n-dimensional grid, connected at (k−1)-dimensional cells. Examples:
|2||1||polyline or polystick|
One can further generalize polyominoids by specifying the dimension of their cell connections. For example, a polyking may be regarded as a (2,2,0)-polyominoid.
Here I show all (3,2)-polyominoids with at most 4 cells. Like polycubes, polyominoids may be one-sided or two-sided. One-sided means that distinct mirror images are counted as different polyominoids. Two-sided means that distinct mirror images are counted as the same polyominoid.
The diagrams below show the two-sided polyominoids.
Last revised 2022-05-31.