This page is just a reference for the list of uniform polypeta. All information is based on Jonathan Bowers' polypeton website and Richard Klitzing's polytope website.
Updates 2014:
- 3 May – Created this main page.
Listing
edit- Category A: Prisms (1292 polypeta) – there's one prism for every uniform polypeton, except the penteract from category 1, so there are 1292 of these.
- Category B: Choriogonal Duoprisms (∞ polypeta) – polychoron-polygon duoprisms.
- Category C: Hedral Duoprisms (2849 polypeta) – polyhedron-polyhedron duoprisms.
- Category D: Hedrigonal Dippips (∞ polypeta) – prisms of polyteron category B.
- Category E: Hedral Antiprism Duoprisms (∞ polypeta) – antiprism-polyhedron duoprisms.
- Category F: Antiprism Duoprisms (∞ polypeta) – antiprism-antiprism duoprisms.
- Category G: Antiprismigonal Dippips (∞ polypeta) – prisms of polyteron category C.
- Category H: Trioprisms (∞ polypeta) – polygon-polygon-polygon triaprisms.
- Category 1: Primaries (Polypeta 1 − 111) – The 3 regular polypeta, the demihexeract, the E6 polytope, 122 polytope, and their facetings.
- Category 2: Truncates (Polypeta 112 – 144) – Truncates, bitruncates, and tritruncates.
- Category 3: Rectates (Polypeta 145 – 324) – Rectified and birectified heptapeton, rectified hexeract, rectified hexacross, and their regiments.
- Category 4: Brox Regiment (Polypeta 325 – ???) – Regiment of the birectified hexeract. Count may be four- or five-digit.
- Category 5: Brag Regiment (??? polypeta) – Regiment of the birectified hexacross. Count may be four- or five-digit.
- Category 6: Jak Rectates (??? polypeta) – Regiments of rectified E6 and rectified 122. Count may be four-, five-digit, or even six-digit.
- Category 7: Tet Sphenoverts (93 polypeta) – Regiments of cantellated heptapeton, cantellated hexeract, and quasicantellated hexeract.
- Category 8: Grand Sphenoverts (??? polypeta) – Regiments of cantellated hexacross (290) and cantellated E6 (four- or five-digit?).
- Category 9: Birhombates (??? polypeta) – Bicantellates and regiments.
- Category 10: Podiumverts (97 polypeta) – Pentellates and regiments.
- Category 11: Fastegiumverts (953 polypeta) – Stericates and regiments.
- Category 12: Dippifastegiumverts (??? polypeta) – Runcinates and regiments.
- Category 13: Duofastegiumverts (??? polypeta) – Biruncinates and regiments.
- Category 14: Cupoliverts (1933 polypeta) – Regiments of xoo8x, oo6ox, xo8ox. Four-digit in total?
- Category 15: Cupogiumverts (??? polypeta) – Regiments of oxo8x, ox8ox. Four-digit or five-digit in total?
- Category 16: Greater Truncates (57 polypeta) – Cantitruncates, runcicantitruncates, bicantitruncates, steriruncicantitruncates, biruncicantitruncates, omnitruncates.
- Category 17: Prismatotruncates (184 polypeta) – Regiments of prismatotruncates.
- Category 18: Prismatorhombates and Kin (102 polypeta) – Runcicantellates, steriruncitruncates, steriruncicantellates, pentiruncicantitruncates, pentistericantitruncates, etc.
- Category 19: Celliprismates and Kin (115 polypeta) – Steriruncinates, penticantitruncates, pentisteritruncates, etc.
- Category 20: Sphenic Pyriverts (92 polypeta) – Biruncicantellates, stericantitruncates, etc.
- Category 21: Tericellates (75 polypeta) – Pentistericates.
- Category 22: Cellitruncates (270 polypeta) – Steritruncates.
- Category 23: Cellirhombates (348 polypeta) – Stericantellates (three- or four-digit in total?).
- Category 24: Teraprismates (835 polypeta) – Penticantellates.
- Category 25: Antisphenopyriverts (153 polypeta) – Pentiruncitruncates.
- Category 26: Trapezoidal Duodispheniverts (24 polypeta) – Pentiruncicantellates.
- Category 27: Cophix and Catjak Regiments (112 polypeta) – Regiments of xxo8x and xo8xx.
- Category 28: Skewed Sphenic Pyriverts (90 polypeta) – Regiments of xxxG, xxGx, xGxx, oxxG, xGxo, xx6xx.
- Category 29: Skewed Prismatotruncates (189 polypeta) – Regiments of oxGx, xxGo, ox6xx.
- Category 30: Skewed Fastegipyriverts (399 polypeta) – Regiments of xxoG, xoGx, xo6xx.
- Category 31: Scrokix and Gacrokix Regiments (342 polypeta) – Regiments of xoxG, xGox. Total count three-, four-, or five-digit?
- Category 32: Drokix, Srokix, and Grokix Regiments (1021 polypeta) – Regiments of oxGo, ooxG, xGoo.
- Category 33: Gipkix, Sipkix, and Spojak Regiments (??? polypeta) – Regiments of xoGo, oxoG, ox6ox. Total count four- or five-digit?
- Category 34: Cakix Regiment (781 polypeta) – Cakix is xooG.
- Category 35: Sram Regiment (287 polypeta) – Sram is ox6xo (cantellated 122).
- Category 36: Spam Regiment (??? polypeta) – Spam is xo6ox (runcinated 122). Count probably four-digit, which, as Bowers notes, is quite fitting for the short name of this polypeton.
- Category 37: Sabrim Regiment (??? polypeta) – Sabrim is xo9ox (bicantellated 122). Count probably four-digit.
- Category 38: Miscellaneous (16 polypeta) – Ontip and gontip regiments (6D versions of 4D's ondip and gondip, which can be found in polychoron category 20 as #1846–#1849).