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The dual of a non-convex polyhedron is also a non-convex polyhedron. [2] ( By contraposition.) There are ten non-convex isotoxal polyhedra based on the quasiregular octahedron, cuboctahedron, and icosidodecahedron: the five (quasiregular) hemipolyhedra based on the quasiregular octahedron, cuboctahedron, and icosidodecahedron, and their five (infinite) duals:
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§6.2 Isohedral tiling, §6.3 isogonal tiling, §6.4 isotoxal tiling, list of isotoxal tilings, §6.5 striped pattern, §6.6 Evgraf Fedorov, Alexei Vasilievich Shubnikov, planigon, Boris Delone: 7: Classification with respect to symmetries §7.1 Conjugate element, §7.7 arrangement of lines, §7.8 Circle packing: 8: Colored patterns and tilings
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