From Wikipedia, the free encyclopedia
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.
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).