Nature

Nature is a concept created by Jonathan Bowers to describe if a polytope has three or more elements of a given dimension that both lie in the same space in the next dimension, and share an element of the previous dimension. There are three natures of polytopes: Tame, Feral, and Wild. This can be determined from looking at the (d-3) dimensional element figures of a d-dimensional polytope.

A polytope is said to be tame if there are no such cases - for example, no three faces in a polychoron that both are in the same 3-space and meet at an edge. A tame polychoron will have no edge figures with 3 colinear points. All convex polytopes are tame, and every uniform polyhedron is tame.

A polyope is said to be feral if there are cases of this happening (for example three faces in the same 3-space and meeting at an edge), but the space doesn't have an actual element (so there is no actuall cell there. A feral polychoron has edge figures with three colinear points, but there is no actual line there. Any polytoope that does have a cell there is said to be wild. Wild polychora have edge figures with three colinear points and an edge connecthing there.