User:Tomruen/Scaliforms

Wythoff constructions with alternations produce vertex-transitive figures that can be made equilateral, but not uniform because the alternated gaps (around the removed vertices) create cells that are not regular or semiregular. A proposed name for such figures is scaliform polytopes. This category allows a subset of Johnson solids as cells, for example triangular cupola.

Each vertex configuration within a Johnson solid must exist within the vertex figure. For example, a square pyramid has two vertex configurations: 3.3.4 around the base, and 3.3.3.3 at the apex.

The symmetry order of a vertex-transitive polytope is the number of vertices times the symmetry order of the vertex figure.

The scaliforms and some related non-Wythoffian 4-polytopes are give below: