Polyform

==Generalizations==

==Generalizations==

Polyforms can also be considered in higher dimensions. In 3-dimensional space, basic [[polyhedra]] can be joined along congruent faces. Joining [[cube (geometry)|cube]]s in this way produces the [[polycube]]s, and joining [[tetrahedron]]s in this way produces the polytetrahedrons.

Polyforms can also be considered in higher dimensions. In 3-dimensional space, basic [[polyhedra]] can be joined along congruent faces. Joining [[cube (geometry)|cube]]s in this way produces the [[polycube]]s, and joining [[tetrahedron]]s in this way produces the polytetrahedrons. 2-dimensional polyforms can also be folded out of the plane along their edges, in similar fashion to a [[Net (polyhedron)|net]]; in the case of polyominoes, this results in [[polyominoid]]s.

One can allow more than one basic polygon. The possibilities are so numerous that the exercise seems pointless, unless extra requirements are brought in. For example, the [[Penrose tile]]s define extra rules for joining edges, resulting in interesting polyforms with a kind of pentagonal symmetry.

One can allow more than one basic polygon. The possibilities are so numerous that the exercise seems pointless, unless extra requirements are brought in. For example, the [[Penrose tile]]s define extra rules for joining edges, resulting in interesting polyforms with a kind of pentagonal symmetry.