About: List of isotoxal polyhedra and tilings

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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.

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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. The dual of an isotoxal polyhedron is also an isotoxal polyhedron. (See the Dual polyhedron article.) (en)
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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. (en)
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  • List of isotoxal polyhedra and tilings (en)
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