Polytopes Wiki
Register
Advertisement
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[]

Tetrahedron
Icosidodecahedron
Great icosahedron
Small cubicuboctahedron

Tetrahedron

Platonic solid

Read more >

Icosidodecahedron

Archimedean solid

Read more >

Great icosahedron

Kepler-Poinsot solid

Read more >

Small cubicuboctahedron

Uniform polyhedron

Read more >

Tetrahedron
Icosidodecahedron
Great icosahedron
Small cubicuboctahedron

Uniform Polyhedra[]

  1. Regulars (1-9)
  2. Truncates (10-19)
  3. Quasiregulars (20-35)
  4. Trapeziverts (36-56)
  5. Omnitruncates (57-63)
  6. Snubs (64-75)
  7. Prisms and Antiprisms

Non-uniform Finite Polyhedra[]

Skew Polyhedra[]

3D Honeycombs[]


Polychora[]

Uniform Polychora[]

  1. Regulars (1 - 17)
  2. Truncates (18 - 38)
  3. Triangular rectates (39-59)
  4. Icositetrachoron regiment (60 - 72)
  5. Pentagonal rectates (73 - 132)
  6. Sphenoverts (133 - 297)
  7. Bitruncates (298 - 306)
  8. Grombates (307 - 329)
  9. Omnitruncates (330 - 351)
  10. Prismatorhombates (352 - 441)
  11. Antipodiumverts (442 - 481)
  12. Podiumverts (482 - 511)
  13. Squapverts (512 - 551)
  14. Skewverts (552 - 611)
  15. Antifrustary distetracontoctachoron regiment (612 - 664)
  16. Antifrustary hexacosatrishecatonicosachoron regiment (665 - 763)
  17. Small stellated hecatonicosachoron regiment (764 - 777)
  18. Ditetrahedrals (778 - 888)
  19. Prisms (889 - 962)
  20. Miscellaneous polychora 1 (963 - 984)
  21. Prismated dishecatonicosachoron regiment (985 - 1065)
  22. Great dipentary trishecatonicosachoron regiment (1066 - 1146)
  23. Rectified small ditrigonary hexacosahecatonicosachoron regiment (1147 - 1303)
  24. Small tritrigonary prismatohecatonicosadishexacosachoron regiment (1304 - 1382)
  25. Great tritrigonary hexacosatrishecatonicosachoron regiment (1383 - 1461)
  26. Blends (1462 - 1473)
  27. Disnubs (Sidtaps and gidtaps) (1474 - 1491)
  28. Inverted dicuboctisnub doubles (idcossids) (1492 - 1668)
  29. Diretrocuboctisnubprismatodiprismatodoubles (dircospids) (1669 - 1845)
  30. Miscellaneous polychora 2 (1846-1855)
  31. 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:


Other polytopes websites[]

Advertisement