User:Double sharp/Polytera
This page is just a reference for the list of uniform polytera. All information is based on Jonathan Bowers' polyteron website and Richard Klitzing's polytope website.
Updates 2013:
- 20 July – Created this main page.
- 24 July – Added categories 1, 2, and 3.
- 5 August – Added links for category 1.
- 10 August – Gave some explanation for the categories, and added category 19.
2014:
- 3 May – Updated listing to reflect new discoveries, especially category 19. Added category 4.
Coming soon: categories 9, 10, 13 (offered on Bowers' website).
Listing
[edit]- Category A: Prisms (Polytera 1294 – 3067) – there's one prism for every uniform polychoron, except the tesseract from category 1 and the prisms from category 19, so there are 1774 of these.
- Category B: Duoprisms – these are the polygon-polyhedron duoprisms.
- Category C: Antiprism-Polygon Duoprisms – self-explanatory. These are the polygon-polygonal antiprism duoprisms.
- Category D: Duoprism Prisms – these are the prisms of the duoprisms (category A from the polychora).
- Category 1: Primaries (Polytera 1 – 12) – the three regular polytera, the demipenteract, and their regiments (uniform facetings).
- Category 2: Truncates (Polytera 13 – 24) – the truncates and the bitruncates, with their regiments.
- Category 3: Rectates (Polytera 25 – 47) – the rectified and birectified hexateron, and the rectified penteract, and their regiments.
- Category 4: Rat Regiment (Polytera 48 – 91) – the regiment of the rectified pentacross.
- Category 5: Nit Regiment (Polytera 92 – 240) – the regiment of the birectified penteract.
- Category 6: Sphenoverts (Polytera 241 – 378) – the cantellates and their regiments.
- Category 7: Birhombates (Polytera 379 – 448) – the bicantellates and their regiments.
- Category 8: Fastegiumverts (Polytera 449 – 681) – the runcinates and their regiments.
- Category 9: Podiumverts (Polytera 682 – 722) – the stericates and their regiments.
- Category 10: Greater Truncates (Polytera 723 – 748) – the great rhombates (cantitruncates), great prismates (runcicantitruncates), great birhombates (bicantitruncates), and great cellates (omnitruncates).
- Category 11: Sphenopyriverts (Polytera 749 – 787) – the runcitruncates and their facetings.
- Category 12: Podipyriverts (Polytera 788 – 829) – the steritruncates and their facetings.
- Category 13: Prismatorhombates and Kin (Polytera 830 – 871) – the runcicantellates, steriruncicantellates, and steriruncitruncates, with their facetings.
- Category 14: Antisphenoverts (Polytera 872 – 943) – the stericantellates and their facetings.
- Category 15: Siphin Regiment (Polytera 944 – 999) – the regiment of the small prismated demipenteract (runcinated demipenteract).
- Category 16: Skivbacadint and Gikvacadint Regiments (Polytera 1000 – 1125) – skivbadant is o3x3o3x4/3x4*c while gikvacadint is x3o3x3o *b4x4/3*c.
- Category 17: Sibacadint and Gidacadint Regiments (Polytera 1126 – 1155) – sibacadint is x3x3o3x4/3x4*c while gidacadint is x3o3x3x *b4x4/3*c.
- Category 18: Skatbacadint Regiment (Polytera 1156 – 1288) – skatbacadint is x3o3o3x4/3x4*c.
- Category 19: Miscellaneous (Polytera 1289 – 1293) – the first two are just the Johnson antiprisms of 5D, which are described at George Olshevsky's Glossary for Hyperspace. The last three are the hosiap regiment, where hosiap is the blend of 6 demipenteracts.