Nature

Nature is a concept created by Jonathan Bowers to differentiate polytopes that have co-spatial elements. There are three categories: Tame, Feral, and Wild that a d-dimensional polytope can have, determined from two properties:


 * There are three (or more) d-elements that share a (d+1) space and a (d-1) element
 * Those d-elements also share a (d+1) element

The category can be determined from looking at the (d-3) element figures of a d-dimensional polytope.

Tame
A polytope is said to be tame if it satisfies neither of the two properties. For example, a polychoron where no three faces are in the same 3-space and meet at an edge. A tame polychoron will have no edge figures with 3 collinear points. All convex polytopes are tame, and every uniform polyhedron is tame.

Feral
A polytope is said to be feral if it satisfies the first case, but not the second. In other words, there are cospatial elements, but they have no (d+1) elements between them. Any polytope with pseudofacets is feral or wild. For example, a feral polychoron has edge figures with three colinear points, but there is no actual line there.

Wild
Any polytope that satisfies both properties is said to be wild. Wild polychora have edge figures with three collinear points and an edge connecting there.