Polyform

In recreational mathematics, a polyform is a plane figure or solid compound constructed by joining together identical basic polygons.

The rules for joining the polygons together may vary, and must therefore be stated for each distinct type of polyform.

2-dimensional polyforms can also be folded out of the plane along their edges, in similar fashion to a net; in the case of polyominoes, this results in polyominoids.

For example, the Penrose tiles define extra rules for joining edges, resulting in interesting polyforms with a kind of pentagonal symmetry.

For instance, squares may be joined orthogonally at vertices, as well as at edges, to form hinged/pseudo-polyominos, also known as polyplets or polykings.