Symmetrohedron

In geometry, a symmetrohedron is a high-symmetry polyhedron containing convex regular polygons on symmetry axes with gaps on the convex hull filled by irregular polygons.

The final parameter, α, controls the relative sizes of the non-degenerate axis-gons.

Conway polyhedron notation is another way to describe these polyhedra, starting with a regular form, and applying prefix operators.

The notation doesn't imply which faces should be made regular beyond the uniform solutions of the Archimedean solids.

Coxeter-Dynkin diagrams exist for these uniform polyhedron solutions, representing the position of the generator point within the fundamental domain.