Welcome to the Polytopes Wiki!
This wiki contains details of the different polytopes
0-dimensions to 2-dimensions[]
The low-dimensional polytopes (points to polygons) are the simplest. As such, they have been collated under one sub-page.
Polyhedra[]
Uniform Polyhedra[]
- Regulars (1-9)
- Truncates (10-19)
- Quasiregulars (20-35)
- Trapeziverts (36-56)
- Omnitruncates (57-63)
- Snubs (64-75)
- Prisms and Antiprisms
- Degenerates
- Compounds
Non-uniform Finite Polyhedra[]
- Johnson solids
- Archimedean duals
- Stellations
- Facets
Skew Polyhedra[]
3D Honeycombs[]
Polychora[]
Uniform Polychora[]
- Regulars (1 - 17)
- Truncates (18 - 38)
- Triangular rectates (39-59)
- Icositetrachoron regiment (60 - 72)
- Pentagonal rectates (73 - 132)
- Sphenoverts (133 - 297)
- Bitruncates (298 - 306)
- Grombates (307 - 329)
- Omnitruncates (330 - 351)
- Prismatorhombates (352 - 441)
- Antipodiumverts (442 - 481)
- Podiumverts (482 - 511)
- Squapverts (512 - 551)
- Skewverts (552 - 611)
- Antifrustary distetracontoctachoron regiment (612 - 664)
- Antifrustary hexacosatrishecatonicosachoron regiment (665 - 763)
- Small stellated hecatonicosachoron regiment (764 - 777)
- Ditetrahedrals (778 - 888)
- Prisms (889 - 962)
- Miscellaneous polychora 1 (963 - 984)
- Prismated dishecatonicosachoron regiment (985 - 1065)
- Great dipentary trishecatonicosachoron regiment (1066 - 1146)
- Rectified small ditrigonary hexacosahecatonicosachoron regiment (1147 - 1303)
- Small tritrigonary prismatohecatonicosadishexacosachoron regiment (1304 - 1382)
- Great tritrigonary hexacosatrishecatonicosachoron regiment (1383 - 1461)
- Blends (1462 - 1473)
- Disnubs (Sidtaps and gidtaps) (1474 - 1491)
- Inverted dicuboctisnub doubles (idcossids) (1492 - 1668)
- Diretrocuboctisnubprismatodiprismatodoubles (dircospids) (1669 - 1845)
- Miscellaneous polychora 2 (1846-1855)
- Snub disoctachora (1856-2188)
Infinite series[]
As well as making a prism from the 3D prisms and antiprisms, there are two other infinite categories of uniform polychora.
A. Duoprisms
B. Antiduoprisms
CRF polychora[]
The CRF (Convex Regular-Faced) polychora are the 4D analgue of the 3D Johnson polyhedra.
Annexes[]
Other pages available are:
- Definitions
- List of uniform polyhedra by army
- Schwarz triangles
- List of Goursat tetrahedra
- Code used to generate the images, etc.
Other polytopes websites[]
- www.polytope.net: This is a comprehensive web site, giving lots of useful information
- bendwavy.org
- eusebeia
- verse-and-dimensions.fandom.com: wiki site
- hi.gher.space: wiki site
- polytope.miraheze.org: wiki site, “The Polytope Wiki is a wiki dedicated to the classification, description, and discovery of polytopes.”
- wikipedia
- polytope discord