Isotoxal polytope

A polytope is isotoxal or edge-transitive if its edges are identical under its symmetry group. In other words, given any two edges, there is a symmetry of the polytope that transforms one into the other. Clearly, an isotoxal polytope must have only one edge length. Isotoxal polytopes as a group are much less studied than isotopic (vertex-transitive) and isogonal (facet-transitive) polytopes.

Most isotoxal polygons have degrees of freedom, i.e. their vertex locations can be continuously varied. Non-regular isotoxal polygons have an even number of vertices, which lie on two concentric circles and alternate between the two circles in a zigzag.

Gordon Collins investigated isotoxal polyhedra and compounds, producing the most comprehensive enumeration as of 2023.