B7 polytope
# B7 polytope

Orthographic projections in the $B_7$ Coxeter plane :

| 7-cube | 7-orthoplex | 7-demicube |
| - | - | - |

In 7-dimensional geometry, there are 128 uniform polytopes with $B_7$ symmetry. There are two regular forms, the 7-orthoplex, and 8-cube with 14 and 128 vertices respectively. The 7-demicube is added with half of the symmetry.

They can be visualized as symmetric orthographic projections in Coxeter planes of the $B_7$ Coxeter group, and other subgroups.

## Graphs

Symmetric orthographic projections of these 128 polytopes can be made in the $B_7,$ $B_6,$ $B_5,$ $B_4,$ $B_3,$ $B_2,$ $A_5,$ $A_3,$ Coxeter planes. $A_k$ has [k+1] symmetry, and $B_k$ has [2k] symmetry.

These 128 polytopes are each shown in these 8 symmetry planes, with vertices and edges drawn, and vertices colored by the number of overlapping vertices in each projective position.

| # | Coxeter plane graphs | Coxeter plane graphs | Coxeter plane graphs | Coxeter plane graphs | Coxeter plane graphs | Coxeter plane graphs | Coxeter plane graphs | Coxeter plane graphs | Coxeter-Dynkin diagram Schläfli symbol Johnson and Bowers Name |
| - | - | - | - | - | - | - | - | - | - |
| # | $B_7$ [14] | $B_6$ [12] | $B_5$ [10] | $B_4$ [8] | $B_3$ [6] | $B_2$ [4] | $A_5$ [6] | $A_3$ [4] | Coxeter-Dynkin diagram Schläfli symbol Johnson and Bowers Name |
| 1 | | | | | | | | | {3,3,3,3,3,4} 7-orthoplex Hecatonicosoctaexon (zee) |
| 2 | | | | | | | | | $t_1{3,3,3,3,3,4}$ Rectified 7-orthoplex Rectified hecatonicosoctaexon (rez) |
| 3 | | | | | | | | | $t_2{3,3,3,3,3,4}$ Birectified 7-orthoplex Birectified hecatonicosoctaexon (barz) |
| 4 | | | | | | | | | $t_3{4,3,3,3,3,3}$ Trirectified 7-cube Hepteractihecatonicosoctaexon (sez) |
| 5 | | | | | | | | | $t_2{4,3,3,3,3,3}$ Birectified 7-cube Birectified hepteract (bersa) |
| 6 | | | | | | | | | $t_1{4,3,3,3,3,3}$ Rectified 7-cube Rectified hepteract (rasa) |
| 7 | | | | | | | | | {4,3,3,3,3,3} 7-cube Hepteract (hept) |
| 128 | | | | | | | | | h{4,3,3,3,3,3} 7-demicube Hemihepteract |
| 8 | | | | | | | | | $t_{0,1}{3,3,3,3,3,4}$ Truncated 7-orthoplex Truncated hecatonicosoctaexon (Taz) |
| 9 | | | | | | | | | $t_{0,2}{3,3,3,3,3,4}$ Cantellated 7-orthoplex Small rhombated hecatonicosoctaexon (Sarz) |
| 10 | | | | | | | | | $t_{1,2}{3,3,3,3,3,4}$ Bitruncated 7-orthoplex Bitruncated hecatonicosoctaexon (Botaz) |
| 11 | | | | | | | | | $t_{0,3}{3,3,3,3,3,4}$ Runcinated 7-orthoplex Small prismated hecatonicosoctaexon (Spaz) |
| 12 | | | | | | | | | $t_{1,3}{3,3,3,3,3,4}$ Bicantellated 7-orthoplex Small birhombated hecatonicosoctaexon (Sebraz) |
| 13 | | | | | | | | | $t_{2,3}{3,3,3,3,3,4}$ Tritruncated 7-orthoplex Tritruncated hecatonicosoctaexon (Totaz) |
| 14 | | | | | | | | | $t_{0,4}{3,3,3,3,3,4}$ Stericated 7-orthoplex Small cellated hecatonicosoctaexon (Scaz) |
| 15 | | | | | | | | | $t_{1,4}{3,3,3,3,3,4}$ Biruncinated 7-orthoplex Small biprismated hecatonicosoctaexon (Sibpaz) |
| 16 | | | | | | | | | $t_{2,4}{4,3,3,3,3,3}$ Tricantellated 7-cube Small trirhombi-hepteractihecatonicosoctaexon (Strasaz) |
| 17 | | | | | | | | | $t_{2,3}{4,3,3,3,3,3}$ Tritruncated 7-cube Tritruncated hepteract (Tatsa) |
| 18 | | | | | | | | | $t_{0,5}{3,3,3,3,3,4}$ Pentellated 7-orthoplex Small terated hecatonicosoctaexon (Staz) |
| 19 | | | | | | | | | $t_{1,5}{4,3,3,3,3,3}$ Bistericated 7-cube Small bicelli-hepteractihecatonicosoctaexon (Sabcosaz) |
| 20 | | | | | | | | | $t_{1,4}{4,3,3,3,3,3}$ Biruncinated 7-cube Small biprismated hepteract (Sibposa) |
| 21 | | | | | | | | | $t_{1,3}{4,3,3,3,3,3}$ Bicantellated 7-cube Small birhombated hepteract (Sibrosa) |
| 22 | | | | | | | | | $t_{1,2}{4,3,3,3,3,3}$ Bitruncated 7-cube Bitruncated hepteract (Betsa) |
| 23 | | | | | | | | | $t_{0,6}{4,3,3,3,3,3}$ Hexicated 7-cube Small peti-hepteractihecatonicosoctaexon (Suposaz) |
| 24 | | | | | | | | | $t_{0,5}{4,3,3,3,3,3}$ Pentellated 7-cube Small terated hepteract (Stesa) |
| 25 | | | | | | | | | $t_{0,4}{4,3,3,3,3,3}$ Stericated 7-cube Small cellated hepteract (Scosa) |
| 26 | | | | | | | | | $t_{0,3}{4,3,3,3,3,3}$ Runcinated 7-cube Small prismated hepteract (Spesa) |
| 27 | | | | | | | | | $t_{0,2}{4,3,3,3,3,3}$ Cantellated 7-cube Small rhombated hepteract (Sersa) |
| 28 | | | | | | | | | $t_{0,1}{4,3,3,3,3,3}$ Truncated 7-cube Truncated hepteract (Tasa) |
| 29 | | | | | | | | | $t_{0,1,2}{3,3,3,3,3,4}$ Cantitruncated 7-orthoplex Great rhombated hecatonicosoctaexon (Garz) |
| 30 | | | | | | | | | $t_{0,1,3}{3,3,3,3,3,4}$ Runcitruncated 7-orthoplex Prismatotruncated hecatonicosoctaexon (Potaz) |
| 31 | | | | | | | | | $t_{0,2,3}{3,3,3,3,3,4}$ Runcicantellated 7-orthoplex Prismatorhombated hecatonicosoctaexon (Parz) |
| 32 | | | | | | | | | $t_{1,2,3}{3,3,3,3,3,4}$ Bicantitruncated 7-orthoplex Great birhombated hecatonicosoctaexon (Gebraz) |
| 33 | | | | | | | | | $t_{0,1,4}{3,3,3,3,3,4}$ Steritruncated 7-orthoplex Cellitruncated hecatonicosoctaexon (Catz) |
| 34 | | | | | | | | | $t_{0,2,4}{3,3,3,3,3,4}$ Stericantellated 7-orthoplex Cellirhombated hecatonicosoctaexon (Craze) |
| 35 | | | | | | | | | $t_{1,2,4}{3,3,3,3,3,4}$ Biruncitruncated 7-orthoplex Biprismatotruncated hecatonicosoctaexon (Baptize) |
| 36 | | | | | | | | | $t_{0,3,4}{3,3,3,3,3,4}$ Steriruncinated 7-orthoplex Celliprismated hecatonicosoctaexon (Copaz) |
| 37 | | | | | | | | | $t_{1,3,4}{3,3,3,3,3,4}$ Biruncicantellated 7-orthoplex Biprismatorhombated hecatonicosoctaexon (Boparz) |
| 38 | | | | | | | | | $t_{2,3,4}{4,3,3,3,3,3}$ Tricantitruncated 7-cube Great trirhombi-hepteractihecatonicosoctaexon (Gotrasaz) |
| 39 | | | | | | | | | $t_{0,1,5}{3,3,3,3,3,4}$ Pentitruncated 7-orthoplex Teritruncated hecatonicosoctaexon (Tetaz) |
| 40 | | | | | | | | | $t_{0,2,5}{3,3,3,3,3,4}$ Penticantellated 7-orthoplex Terirhombated hecatonicosoctaexon (Teroz) |
| 41 | | | | | | | | | $t_{1,2,5}{3,3,3,3,3,4}$ Bisteritruncated 7-orthoplex Bicellitruncated hecatonicosoctaexon (Boctaz) |
| 42 | | | | | | | | | $t_{0,3,5}{3,3,3,3,3,4}$ Pentiruncinated 7-orthoplex Teriprismated hecatonicosoctaexon (Topaz) |
| 43 | | | | | | | | | $t_{1,3,5}{4,3,3,3,3,3}$ Bistericantellated 7-cube Bicellirhombi-hepteractihecatonicosoctaexon (Bacresaz) |
| 44 | | | | | | | | | $t_{1,3,4}{4,3,3,3,3,3}$ Biruncicantellated 7-cube Biprismatorhombated hepteract (Bopresa) |
| 45 | | | | | | | | | $t_{0,4,5}{3,3,3,3,3,4}$ Pentistericated 7-orthoplex Tericellated hecatonicosoctaexon (Tocaz) |
| 46 | | | | | | | | | $t_{1,2,5}{4,3,3,3,3,3}$ Bisteritruncated 7-cube Bicellitruncated hepteract (Bactasa) |
| 47 | | | | | | | | | $t_{1,2,4}{4,3,3,3,3,3}$ Biruncitruncated 7-cube Biprismatotruncated hepteract (Biptesa) |
| 48 | | | | | | | | | $t_{1,2,3}{4,3,3,3,3,3}$ Bicantitruncated 7-cube Great birhombated hepteract (Gibrosa) |
| 49 | | | | | | | | | $t_{0,1,6}{3,3,3,3,3,4}$ Hexitruncated 7-orthoplex Petitruncated hecatonicosoctaexon (Putaz) |
| 50 | | | | | | | | | $t_{0,2,6}{3,3,3,3,3,4}$ Hexicantellated 7-orthoplex Petirhombated hecatonicosoctaexon (Puraz) |
| 51 | | | | | | | | | $t_{0,4,5}{4,3,3,3,3,3}$ Pentistericated 7-cube Tericellated hepteract (Tacosa) |
| 52 | | | | | | | | | $t_{0,3,6}{4,3,3,3,3,3}$ Hexiruncinated 7-cube Petiprismato-hepteractihecatonicosoctaexon (Pupsez) |
| 53 | | | | | | | | | $t_{0,3,5}{4,3,3,3,3,3}$ Pentiruncinated 7-cube Teriprismated hepteract (Tapsa) |
| 54 | | | | | | | | | $t_{0,3,4}{4,3,3,3,3,3}$ Steriruncinated 7-cube Celliprismated hepteract (Capsa) |
| 55 | | | | | | | | | $t_{0,2,6}{4,3,3,3,3,3}$ Hexicantellated 7-cube Petirhombated hepteract (Purosa) |
| 56 | | | | | | | | | $t_{0,2,5}{4,3,3,3,3,3}$ Penticantellated 7-cube Terirhombated hepteract (Tersa) |
| 57 | | | | | | | | | $t_{0,2,4}{4,3,3,3,3,3}$ Stericantellated 7-cube Cellirhombated hepteract (Carsa) |
| 58 | | | | | | | | | $t_{0,2,3}{4,3,3,3,3,3}$ Runcicantellated 7-cube Prismatorhombated hepteract (Parsa) |
| 59 | | | | | | | | | $t_{0,1,6}{4,3,3,3,3,3}$ Hexitruncated 7-cube Petitruncated hepteract (Putsa) |
| 60 | | | | | | | | | $t_{0,1,5}{4,3,3,3,3,3}$ Pentitruncated 7-cube Teritruncated hepteract (Tetsa) |
| 61 | | | | | | | | | $t_{0,1,4}{4,3,3,3,3,3}$ Steritruncated 7-cube Cellitruncated hepteract (Catsa) |
| 62 | | | | | | | | | $t_{0,1,3}{4,3,3,3,3,3}$ Runcitruncated 7-cube Prismatotruncated hepteract (Petsa) |
| 63 | | | | | | | | | $t_{0,1,2}{4,3,3,3,3,3}$ Cantitruncated 7-cube Great rhombated hepteract (Gersa) |
| 64 | | | | | | | | | $t_{0,1,2,3}{3,3,3,3,3,4}$ Runcicantitruncated 7-orthoplex Great prismated hecatonicosoctaexon (Gopaz) |
| 65 | | | | | | | | | $t_{0,1,2,4}{3,3,3,3,3,4}$ Stericantitruncated 7-orthoplex Celligreatorhombated hecatonicosoctaexon (Cogarz) |
| 66 | | | | | | | | | $t_{0,1,3,4}{3,3,3,3,3,4}$ Steriruncitruncated 7-orthoplex Celliprismatotruncated hecatonicosoctaexon (Captaz) |
| 67 | | | | | | | | | $t_{0,2,3,4}{3,3,3,3,3,4}$ Steriruncicantellated 7-orthoplex Celliprismatorhombated hecatonicosoctaexon (Caparz) |
| 68 | | | | | | | | | $t_{1,2,3,4}{3,3,3,3,3,4}$ Biruncicantitruncated 7-orthoplex Great biprismated hecatonicosoctaexon (Gibpaz) |
| 69 | | | | | | | | | $t_{0,1,2,5}{3,3,3,3,3,4}$ Penticantitruncated 7-orthoplex Terigreatorhombated hecatonicosoctaexon (Tograz) |
| 70 | | | | | | | | | $t_{0,1,3,5}{3,3,3,3,3,4}$ Pentiruncitruncated 7-orthoplex Teriprismatotruncated hecatonicosoctaexon (Toptaz) |
| 71 | | | | | | | | | $t_{0,2,3,5}{3,3,3,3,3,4}$ Pentiruncicantellated 7-orthoplex Teriprismatorhombated hecatonicosoctaexon (Toparz) |
| 72 | | | | | | | | | $t_{1,2,3,5}{3,3,3,3,3,4}$ Bistericantitruncated 7-orthoplex Bicelligreatorhombated hecatonicosoctaexon (Becogarz) |
| 73 | | | | | | | | | $t_{0,1,4,5}{3,3,3,3,3,4}$ Pentisteritruncated 7-orthoplex Tericellitruncated hecatonicosoctaexon (Tacotaz) |
| 74 | | | | | | | | | $t_{0,2,4,5}{3,3,3,3,3,4}$ Pentistericantellated 7-orthoplex Tericellirhombated hecatonicosoctaexon (Tocarz) |
| 75 | | | | | | | | | $t_{1,2,4,5}{4,3,3,3,3,3}$ Bisteriruncitruncated 7-cube Bicelliprismatotrunki-hepteractihecatonicosoctaexon (Bocaptosaz) |
| 76 | | | | | | | | | $t_{0,3,4,5}{3,3,3,3,3,4}$ Pentisteriruncinated 7-orthoplex Tericelliprismated hecatonicosoctaexon (Tecpaz) |
| 77 | | | | | | | | | $t_{1,2,3,5}{4,3,3,3,3,3}$ Bistericantitruncated 7-cube Bicelligreatorhombated hepteract (Becgresa) |
| 78 | | | | | | | | | $t_{1,2,3,4}{4,3,3,3,3,3}$ Biruncicantitruncated 7-cube Great biprismated hepteract (Gibposa) |
| 79 | | | | | | | | | $t_{0,1,2,6}{3,3,3,3,3,4}$ Hexicantitruncated 7-orthoplex Petigreatorhombated hecatonicosoctaexon (Pugarez) |
| 80 | | | | | | | | | $t_{0,1,3,6}{3,3,3,3,3,4}$ Hexiruncitruncated 7-orthoplex Petiprismatotruncated hecatonicosoctaexon (Papataz) |
| 81 | | | | | | | | | $t_{0,2,3,6}{3,3,3,3,3,4}$ Hexiruncicantellated 7-orthoplex Petiprismatorhombated hecatonicosoctaexon (Puparez) |
| 82 | | | | | | | | | $t_{0,3,4,5}{4,3,3,3,3,3}$ Pentisteriruncinated 7-cube Tericelliprismated hepteract (Tecpasa) |
| 83 | | | | | | | | | $t_{0,1,4,6}{3,3,3,3,3,4}$ Hexisteritruncated 7-orthoplex Peticellitruncated hecatonicosoctaexon (Pucotaz) |
| 84 | | | | | | | | | $t_{0,2,4,6}{4,3,3,3,3,3}$ Hexistericantellated 7-cube Peticellirhombi-hepteractihecatonicosoctaexon (Pucrosaz) |
| 85 | | | | | | | | | $t_{0,2,4,5}{4,3,3,3,3,3}$ Pentistericantellated 7-cube Tericellirhombated hepteract (Tecresa) |
| 86 | | | | | | | | | $t_{0,2,3,6}{4,3,3,3,3,3}$ Hexiruncicantellated 7-cube Petiprismatorhombated hepteract (Pupresa) |
| 87 | | | | | | | | | $t_{0,2,3,5}{4,3,3,3,3,3}$ Pentiruncicantellated 7-cube Teriprismatorhombated hepteract (Topresa) |
| 88 | | | | | | | | | $t_{0,2,3,4}{4,3,3,3,3,3}$ Steriruncicantellated 7-cube Celliprismatorhombated hepteract (Copresa) |
| 89 | | | | | | | | | $t_{0,1,5,6}{4,3,3,3,3,3}$ Hexipentitruncated 7-cube Petiteritrunki-hepteractihecatonicosoctaexon (Putatosez) |
| 90 | | | | | | | | | $t_{0,1,4,6}{4,3,3,3,3,3}$ Hexisteritruncated 7-cube Peticellitruncated hepteract (Pacutsa) |
| 91 | | | | | | | | | $t_{0,1,4,5}{4,3,3,3,3,3}$ Pentisteritruncated 7-cube Tericellitruncated hepteract (Tecatsa) |
| 92 | | | | | | | | | $t_{0,1,3,6}{4,3,3,3,3,3}$ Hexiruncitruncated 7-cube Petiprismatotruncated hepteract (Pupetsa) |
| 93 | | | | | | | | | $t_{0,1,3,5}{4,3,3,3,3,3}$ Pentiruncitruncated 7-cube Teriprismatotruncated hepteract (Toptosa) |
| 94 | | | | | | | | | $t_{0,1,3,4}{4,3,3,3,3,3}$ Steriruncitruncated 7-cube Celliprismatotruncated hepteract (Captesa) |
| 95 | | | | | | | | | $t_{0,1,2,6}{4,3,3,3,3,3}$ Hexicantitruncated 7-cube Petigreatorhombated hepteract (Pugrosa) |
| 96 | | | | | | | | | $t_{0,1,2,5}{4,3,3,3,3,3}$ Penticantitruncated 7-cube Terigreatorhombated hepteract (Togresa) |
| 97 | | | | | | | | | $t_{0,1,2,4}{4,3,3,3,3,3}$ Stericantitruncated 7-cube Celligreatorhombated hepteract (Cogarsa) |
| 98 | | | | | | | | | $t_{0,1,2,3}{4,3,3,3,3,3}$ Runcicantitruncated 7-cube Great prismated hepteract (Gapsa) |
| 99 | | | | | | | | | $t_{0,1,2,3,4}{3,3,3,3,3,4}$ Steriruncicantitruncated 7-orthoplex Great cellated hecatonicosoctaexon (Gocaz) |
| 100 | | | | | | | | | $t_{0,1,2,3,5}{3,3,3,3,3,4}$ Pentiruncicantitruncated 7-orthoplex Terigreatoprismated hecatonicosoctaexon (Tegopaz) |
| 101 | | | | | | | | | $t_{0,1,2,4,5}{3,3,3,3,3,4}$ Pentistericantitruncated 7-orthoplex Tericelligreatorhombated hecatonicosoctaexon (Tecagraz) |
| 102 | | | | | | | | | $t_{0,1,3,4,5}{3,3,3,3,3,4}$ Pentisteriruncitruncated 7-orthoplex Tericelliprismatotruncated hecatonicosoctaexon (Tecpotaz) |
| 103 | | | | | | | | | $t_{0,2,3,4,5}{3,3,3,3,3,4}$ Pentisteriruncicantellated 7-orthoplex Tericelliprismatorhombated hecatonicosoctaexon (Tacparez) |
| 104 | | | | | | | | | $t_{1,2,3,4,5}{4,3,3,3,3,3}$ Bisteriruncicantitruncated 7-cube Great bicelli-hepteractihecatonicosoctaexon (Gabcosaz) |
| 105 | | | | | | | | | $t_{0,1,2,3,6}{3,3,3,3,3,4}$ Hexiruncicantitruncated 7-orthoplex Petigreatoprismated hecatonicosoctaexon (Pugopaz) |
| 106 | | | | | | | | | $t_{0,1,2,4,6}{3,3,3,3,3,4}$ Hexistericantitruncated 7-orthoplex Peticelligreatorhombated hecatonicosoctaexon (Pucagraz) |
| 107 | | | | | | | | | $t_{0,1,3,4,6}{3,3,3,3,3,4}$ Hexisteriruncitruncated 7-orthoplex Peticelliprismatotruncated hecatonicosoctaexon (Pucpotaz) |
| 108 | | | | | | | | | $t_{0,2,3,4,6}{4,3,3,3,3,3}$ Hexisteriruncicantellated 7-cube Peticelliprismatorhombi-hepteractihecatonicosoctaexon (Pucprosaz) |
| 109 | | | | | | | | | $t_{0,2,3,4,5}{4,3,3,3,3,3}$ Pentisteriruncicantellated 7-cube Tericelliprismatorhombated hepteract (Tocpresa) |
| 110 | | | | | | | | | $t_{0,1,2,5,6}{3,3,3,3,3,4}$ Hexipenticantitruncated 7-orthoplex Petiterigreatorhombated hecatonicosoctaexon (Putegraz) |
| 111 | | | | | | | | | $t_{0,1,3,5,6}{4,3,3,3,3,3}$ Hexipentiruncitruncated 7-cube Petiteriprismatotrunki-hepteractihecatonicosoctaexon (Putpetsaz) |
| 112 | | | | | | | | | $t_{0,1,3,4,6}{4,3,3,3,3,3}$ Hexisteriruncitruncated 7-cube Peticelliprismatotruncated hepteract (Pucpetsa) |
| 113 | | | | | | | | | $t_{0,1,3,4,5}{4,3,3,3,3,3}$ Pentisteriruncitruncated 7-cube Tericelliprismatotruncated hepteract (Tecpetsa) |
| 114 | | | | | | | | | $t_{0,1,2,5,6}{4,3,3,3,3,3}$ Hexipenticantitruncated 7-cube Petiterigreatorhombated hepteract (Putgresa) |
| 115 | | | | | | | | | $t_{0,1,2,4,6}{4,3,3,3,3,3}$ Hexistericantitruncated 7-cube Peticelligreatorhombated hepteract (Pucagrosa) |
| 116 | | | | | | | | | $t_{0,1,2,4,5}{4,3,3,3,3,3}$ Pentistericantitruncated 7-cube Tericelligreatorhombated hepteract (Tecgresa) |
| 117 | | | | | | | | | $t_{0,1,2,3,6}{4,3,3,3,3,3}$ Hexiruncicantitruncated 7-cube Petigreatoprismated hepteract (Pugopsa) |
| 118 | | | | | | | | | $t_{0,1,2,3,5}{4,3,3,3,3,3}$ Pentiruncicantitruncated 7-cube Terigreatoprismated hepteract (Togapsa) |
| 119 | | | | | | | | | $t_{0,1,2,3,4}{4,3,3,3,3,3}$ Steriruncicantitruncated 7-cube Great cellated hepteract (Gacosa) |
| 120 | | | | | | | | | $t_{0,1,2,3,4,5}{3,3,3,3,3,4}$ Pentisteriruncicantitruncated 7-orthoplex Great terated hecatonicosoctaexon (Gotaz) |
| 121 | | | | | | | | | $t_{0,1,2,3,4,6}{3,3,3,3,3,4}$ Hexisteriruncicantitruncated 7-orthoplex Petigreatocellated hecatonicosoctaexon (Pugacaz) |
| 122 | | | | | | | | | $t_{0,1,2,3,5,6}{3,3,3,3,3,4}$ Hexipentiruncicantitruncated 7-orthoplex Petiterigreatoprismated hecatonicosoctaexon (Putgapaz) |
| 123 | | | | | | | | | $t_{0,1,2,4,5,6}{4,3,3,3,3,3}$ Hexipentistericantitruncated 7-cube Petitericelligreatorhombi-hepteractihecatonicosoctaexon (Putcagrasaz) |
| 124 | | | | | | | | | $t_{0,1,2,3,5,6}{4,3,3,3,3,3}$ Hexipentiruncicantitruncated 7-cube Petiterigreatoprismated hepteract (Putgapsa) |
| 125 | | | | | | | | | $t_{0,1,2,3,4,6}{4,3,3,3,3,3}$ Hexisteriruncicantitruncated 7-cube Petigreatocellated hepteract (Pugacasa) |
| 126 | | | | | | | | | $t_{0,1,2,3,4,5}{4,3,3,3,3,3}$ Pentisteriruncicantitruncated 7-cube Great terated hepteract (Gotesa) |
| 127 | | | | | | | | | $t_{0,1,2,3,4,5,6}{4,3,3,3,3,3}$ Omnitruncated 7-cube Great peti-hepteractihecatonicosoctaexon (Guposaz) |
