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- Quasiregular_polyhedron abstract "In geometry, a quasiregular polyhedron is a semiregular polyhedron that has exactly two kinds of regular faces, which alternate around each vertex. They are edge-transitive and hence a step closer to regular polyhedra than the semiregular which are merely vertex-transitive.There are only two convex quasiregular polyhedra, the cuboctahedron and the icosidodecahedron. Their names, given by Kepler, come from recognizing their faces contain all the faces of the dual-pair cube and octahedron, in the first, and the dual-pair icosahedron and dodecahedron in the second case.These forms representing a pair of a regular figure and its dual can be given a vertical Schläfli symbol or r{p,q} to represent their containing the faces of both the regular {p,q} and dual regular {q,p}. A quasiregular polyhedron with this symbol will have a vertex configuration p.q.p.q (or (p.q)2).More generally, a quasiregular figure can have a vertex configuration (p.q)r, representing r (2 or more) instances of the faces around the vertex.Tilings of the plane can also be quasiregular, specifically the trihexagonal tiling, with vertex configuration (3.6)2. Other quasiregular tilings exist on the hyperbolic plane, like the triheptagonal tiling, (3.7)2. Or more generally, (p.q)2, with 1/p+1/q<1/2.Some regular polyhedra and tilings (those with an even number of faces at each vertex) can also be considered quasiregular by differentiating between faces of the same number of sides, but representing them differently, like having different colors, but no surface features defining their orientation. A regular figure with Schläfli symbol {p,q} can be quasiregular, with vertex configuration (p.p)q/2, if q is even.The octahedron can be considered quasiregular as a tetratetrahedron (2 sets of 4 triangles of the tetrahedron), (3a.3b)2, alternating two colors of triangular faces. Similarly the square tiling (4a.4b)2 can be considered quasiregular, colored as a checkerboard. Also the triangular tiling can have alternately colored triangle faces, (3a.3b)3.".
- Quasiregular_polyhedron thumbnail Uniform_polyhedron-33-t1.png?width=300.
- Quasiregular_polyhedron wikiPageExternalLink quasi-regular-info.html.
- Quasiregular_polyhedron wikiPageID "8810651".
- Quasiregular_polyhedron wikiPageRevisionID "604582225".
- Quasiregular_polyhedron hasPhotoCollection Quasiregular_polyhedron.
- Quasiregular_polyhedron title "Quasiregular polyhedron".
- Quasiregular_polyhedron title "Uniform polyhedron".
- Quasiregular_polyhedron urlname "QuasiregularPolyhedron".
- Quasiregular_polyhedron urlname "UniformPolyhedron".
- Quasiregular_polyhedron subject Category:Quasiregular_polyhedra.
- Quasiregular_polyhedron comment "In geometry, a quasiregular polyhedron is a semiregular polyhedron that has exactly two kinds of regular faces, which alternate around each vertex. They are edge-transitive and hence a step closer to regular polyhedra than the semiregular which are merely vertex-transitive.There are only two convex quasiregular polyhedra, the cuboctahedron and the icosidodecahedron.".
- Quasiregular_polyhedron label "Polyèdre quasi-régulier".
- Quasiregular_polyhedron label "Quasiregular polyhedron".
- Quasiregular_polyhedron label "擬正多面體".
- Quasiregular_polyhedron sameAs Polyèdre_quasi-régulier.
- Quasiregular_polyhedron sameAs 준정다면체.
- Quasiregular_polyhedron sameAs m.027kkl7.
- Quasiregular_polyhedron sameAs Q869652.
- Quasiregular_polyhedron sameAs Q869652.
- Quasiregular_polyhedron wasDerivedFrom Quasiregular_polyhedron?oldid=604582225.
- Quasiregular_polyhedron depiction Uniform_polyhedron-33-t1.png.
- Quasiregular_polyhedron isPrimaryTopicOf Quasiregular_polyhedron.
