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About: List of isotoxal polyhedra and tilings     Goto   Sponge   NotDistinct   Permalink

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In geometry, isotoxal polyhedra and tilings are defined by the property that they have symmetries taking any edge to any other edge. 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.