List of isotoxal polyhedra and tilings
From Wikipedia, the free encyclopedia
In geometry, isotoxal polyhedra and tilings are defined by the property that they have symmetries taking any edge to any other edge.[1] Polyhedra with this property can also be called "edge-transitive", but they should be distinguished from edge-transitive graphs, where the symmetries are combinatorial rather than geometric.
Regular polyhedra are isohedral (face-transitive), isogonal (vertex-transitive), and isotoxal (edge-transitive).
Quasiregular polyhedra are isogonal and isotoxal, but not isohedral; their duals are isohedral and isotoxal, but not isogonal.
The dual of an isotoxal polyhedron is also an isotoxal polyhedron. (See the Dual polyhedron article.)