Semiregular

A semiregular polytope is a uniform polytope that only contains regular facets. The concept was created as a generalization of uniformity in 3D to higher dimensions, but is now superseded by uniform polytopes.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