Semiregular polytope

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 The concept was created as a generalization of uniformity in 3D to higher dimensions, but is now superseded by uniform polytopes.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

• 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

• All nonconvex regular polytopes (sometimes excluded)
• All nonconvex uniform polyhedra
• Conjugates of convex semiregulars
  • The rectified grand hexacosichoron
  • The retrosnub disicositetrachoron
• Facetings of regulars with uniform vertex figures
  • The tesseractihemioctachoron and other demicrosses
  • The small ditrigonary hexacosihecatonicosachoron
  • The ditrigonary dishecatonicosachoron
  • The great ditrigonary hexacosihecatonicosachoron
• Snub facetings of the small stellated hecatonicosachoron
  • The retroantiprismatosnub disicositetrachoron
  • The snub hexecontatetrasnub-snub disoctachoron
  • The snub hecatonicosoctasnub disoctachoron
  • The snub triacontadihexecontatetrasnub disoctachoron
  • The snub hexecontatetrasnub dishexadecachoron
• Ionic decachoric partial faceting of the hecatonicosachoron
  • The tetrasnub antipodic disdecachoron
• Blends of semiregulars
  • The small disnub dishexacosichoron
  • The great disnub dishexacosichoron

Euclidean honeycombs

• 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