Semiregular polytope
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A semiregular polytope is a isogonal polytope that only contains regular facets. The semiregular polytopes are a subset of the uniform polytopes, and the convex semiregular polytopes are a subset of the Blind polytopes. The concept was created as a generalization of uniformity in 3D to higher dimensions, but is now superseded by uniform polytopes. The set of semiregular polytopes is rarely studied.
Convex examples[edit | edit source]
- All convex regular polytopes (sometimes excluded)
- All convex uniform polyhedra (Archimedean solids, prisms, and antiprisms)
- The k21 family in 4 to 8 dimensions
- The rectified pentachoron (021) "tetroctahedric"
- The demipenteract (121) "5-ic semi-regular"
- The 27-72-peton (221) "6-ic semi-regular"
- The 126-576-exon (321) "7-ic semi-regular"
- The 2160-17280-zetton (421) "8-ic semi-regular"
- The rectified hexacosichoron "octicosahedric"
- The snub disicositetrachoron "tetricosahedric"
Nonconvex examples[edit | edit source]
- All nonconvex regular polytopes (sometimes excluded)
- All nonconvex uniform polyhedra
- Conjugates of convex semiregulars
- Facetings of regulars with uniform vertex figures
- Snub facetings of the small stellated hecatonicosachoron
- Ionic decachoric partial faceting of the hecatonicosachoron
- Blends of semiregulars
Euclidean honeycombs[edit | edit source]
- All regular honeycombs (sometimes excluded)
- All uniform tilings of 2-space
- Convex cases
- The tetrahedral-octahedral honeycomb "simple tetroctahedric check"
- The gyrated tetrahedral-octahedral honeycomb "complex tetroctahedric check"
- The gosset octacomb "9-ic check"
- Slab cases
- Any prism product of a hypercube and a hypercubic honeycomb
- The triangular tiling antiprism
- Nonconvex cases
- The cubihemisquare honeycomb and its analogs
- The tetrahedral-hemitriangular honeycomb
- The octahedral-hemitriangular honeycomb
Hyperbolic honeycombs[edit | edit source]
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