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Similarly, a k-isohedral tiling has k separate symmetry orbits (it may contain m different face shapes, for m = k, or only for some m < k). [ 6 ] ("1-isohedral" is the same as "isohedral".) A monohedral polyhedron or monohedral tiling ( m = 1) has congruent faces, either directly or reflectively, which occur in one or more symmetry positions.
Pages in category "Isohedral tilings" The following 76 pages are in this category, out of 76 total. ... Octagonal tiling; Order-1 digonal tiling; Order-2 apeirogonal ...
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.)
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A rhombic dodecahedron is an isohedral and isotoxal polyhedron A great icosidodecahedron is an isogonal and isotoxal star polyhedron A great rhombic triacontahedron is an isohedral and isotoxal star polyhedron The trihexagonal tiling is an isogonal and isotoxal tiling The rhombille tiling is an isohedral and isotoxal tiling with p6m (*632 ...