x1 is a polyform/polyplet/polyomino/polyabolo/polyiamond (etc.) composed of parts/'tile' polytope x2 arranged in (finite) unified shape/pattern x3 in ambient space x4 and subject to rules/restrictions/conditions x5

The number arrangement and rules may be as generic/vague as desired. The number of polytope 'tiles' used can be specified in the third of fifth terbri as desired; the polytopes used need not all be the same, nor regular, so long as the arrangement is meaningful and possible. One of the main differences between rectangular polyplets and polyominoes is that polyominoes cannot have their polytope tiles touching only at their vertices whereas polyplets can (thus, polyominoes are a subset of the rectangular polyplets); this difference can be specified in the final terbri. A tiling of a space may be considered to be an infinite polyform, but that is rather pathological and we can reasonably assume that polyforms referenced by this word will be finite. The polyform is considered to be a unified whole entity. The ambient space is usually going to be the Euclidean space of the same dimension as the polytopes (and the former dimension cannot be exceeded by the latter except in the marginal case of lower-dimensional (id est: hyperplanar) arrangements, in which case parallel cross-sections are really being considered); this space determines the rigid-motion/symmetry isomorphisms of various polyforms (Z and S tetraminoes are non-isomorphic under rigid-motion in the Euclidean plane but are so isomorphic in Euclidean 3-space). The ambient space also determines the expression of (and indeed the 'allowed') polytopes: spherical geometry allows for digons to be arranged so as to form a polyform, but Euclidean 2-space prohibits such objects from the set of possible polygons. The default polytope will probably be a 2-dimensional square; thus the default ambient space will likely be Euclidean 2-space. See also: karda, korfaipletomino

- korfaipletomino
- x1 is a non-polyplet polyform/polyomino/polyabolo/polyiamond (etc.) composed of parts/'tile' polytope x2 arranged in (finite) unified shape/pattern x3 (in which the entirety of sides of polytopes are shared or are not shared at all) in ambient space x4 and subject to rules/restrictions/conditions x5 (implicitly includes the condition of whole sides being shared)