# B7 polytope

 7-cube 7-orthoplex 7-demicube

In 7-dimensional geometry, there are 128 uniform polytopes with B7 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 B7 Coxeter group, and other subgroups.

## Graphs

Symmetric orthographic projections of these 128 polytopes can be made in the B7, B6, B5, B4, B3, B2, A5, A3, Coxeter planes. Ak has [k+1] symmetry, and Bk 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-Dynkin diagram
Schläfli symbol
Johnson and Bowers Name
B7
[14]
B6
[12]
B5
[10]
B4
[8]
B3
[6]
B2
[4]
A5
[6]
A3
[4]
1 80px 80px 80px 80px 80px 80px 80px
{3,3,3,3,3,4}
7-orthoplex
Hecatonicosoctaexon (zee)
2 80px 80px 80px 80px 80px 80px
t1{3,3,3,3,3,4}
Rectified 7-orthoplex
Rectified hecatonicosoctaexon (rez)
3 80px 80px 80px 80px 80px 80px
t2{3,3,3,3,3,4}
Birectified 7-orthoplex
Birectified hecatonicosoctaexon (barz)
4 80px 80px 80px 80px 80px 80px
t3{4,3,3,3,3,3}
Trirectified 7-cube
Hepteractihecatonicosoctaexon (sez)
5 80px 80px 80px 80px 80px 80px
t2{4,3,3,3,3,3}
Birectified 7-cube
Birectified hepteract (bersa)
6 80px 80px 80px 80px 80px 80px
t1{4,3,3,3,3,3}
Rectified 7-cube
Rectified hepteract (rasa)
7 80px 80px 80px 80px 80px 80px 80px
{4,3,3,3,3,3}
7-cube
Hepteract (hept)
128 80px 80px 80px 80px 80px 80px
h{4,3,3,3,3,3}
7-demicube
Hemihepteract
8 80px 80px 80px 80px 80px 80px
t0,1{3,3,3,3,3,4}
Truncated 7-orthoplex
Truncated hecatonicosoctaexon (Taz)
9 80px 80px 80px 80px 80px 80px
t0,2{3,3,3,3,3,4}
Cantellated 7-orthoplex
Small rhombated hecatonicosoctaexon (Sarz)
10 80px 80px 80px 80px 80px 80px
t1,2{3,3,3,3,3,4}
Bitruncated 7-orthoplex
Bitruncated hecatonicosoctaexon (Botaz)
11 80px 80px 80px 80px 80px 80px
t0,3{3,3,3,3,3,4}
Runcinated 7-orthoplex
Small prismated hecatonicosoctaexon (Spaz)
12 80px 80px 80px 80px 80px 80px
t1,3{3,3,3,3,3,4}
Bicantellated 7-orthoplex
Small birhombated hecatonicosoctaexon (Sebraz)
13 80px 80px 80px 80px 80px 80px
t2,3{3,3,3,3,3,4}
Tritruncated 7-orthoplex
Tritruncated hecatonicosoctaexon (Totaz)
14 80px 80px 80px 80px 80px 80px
t0,4{3,3,3,3,3,4}
Stericated 7-orthoplex
Small cellated hecatonicosoctaexon (Scaz)
15 80px 80px 80px 80px 80px 80px
t1,4{3,3,3,3,3,4}
Biruncinated 7-orthoplex
Small biprismated hecatonicosoctaexon (Sibpaz)
16 80px 80px 80px 80px 80px 80px
t2,4{4,3,3,3,3,3}
Tricantellated 7-cube
Small trirhombi-hepteractihecatonicosoctaexon (Strasaz)
17 80px 80px 80px 80px 80px 80px
t2,3{4,3,3,3,3,3}
Tritruncated 7-cube
Tritruncated hepteract (Tatsa)
18 80px 80px 80px 80px 80px 80px
t0,5{3,3,3,3,3,4}
Pentellated 7-orthoplex
Small terated hecatonicosoctaexon (Staz)
19 80px 80px 80px 80px 80px 80px
t1,5{4,3,3,3,3,3}
Bistericated 7-cube
Small bicelli-hepteractihecatonicosoctaexon (Sabcosaz)
20 80px 80px 80px 80px 80px 80px
t1,4{4,3,3,3,3,3}
Biruncinated 7-cube
Small biprismated hepteract (Sibposa)
21 80px 80px 80px 80px 80px 80px
t1,3{4,3,3,3,3,3}
Bicantellated 7-cube
Small birhombated hepteract (Sibrosa)
22 80px 80px 80px 80px 80px 80px
t1,2{4,3,3,3,3,3}
Bitruncated 7-cube
Bitruncated hepteract (Betsa)
23 80px 80px 80px 80px 80px 80px
t0,6{4,3,3,3,3,3}
Hexicated 7-cube
Small peti-hepteractihecatonicosoctaexon (Suposaz)
24 80px 80px 80px 80px 80px 80px
t0,5{4,3,3,3,3,3}
Pentellated 7-cube
Small terated hepteract (Stesa)
25 80px 80px 80px 80px 80px 80px
t0,4{4,3,3,3,3,3}
Stericated 7-cube
Small cellated hepteract (Scosa)
26 80px 80px 80px 80px 80px 80px
t0,3{4,3,3,3,3,3}
Runcinated 7-cube
Small prismated hepteract (Spesa)
27 80px 80px 80px 80px 80px 80px
t0,2{4,3,3,3,3,3}
Cantellated 7-cube
Small rhombated hepteract (Sersa)
28 80px 80px 80px 80px 80px 80px
t0,1{4,3,3,3,3,3}
Truncated 7-cube
Truncated hepteract (Tasa)
29 80px 80px 80px 80px 80px
t0,1,2{3,3,3,3,3,4}
Cantitruncated 7-orthoplex
Great rhombated hecatonicosoctaexon (Garz)
30 80px 80px 80px 80px 80px
t0,1,3{3,3,3,3,3,4}
Runcitruncated 7-orthoplex
Prismatotruncated hecatonicosoctaexon (Potaz)
31 80px 80px 80px 80px 80px
t0,2,3{3,3,3,3,3,4}
Runcicantellated 7-orthoplex
Prismatorhombated hecatonicosoctaexon (Parz)
32 80px 80px 80px 80px 80px
t1,2,3{3,3,3,3,3,4}
Bicantitruncated 7-orthoplex
Great birhombated hecatonicosoctaexon (Gebraz)
33 80px 80px 80px 80px 80px 80px
t0,1,4{3,3,3,3,3,4}
Steritruncated 7-orthoplex
Cellitruncated hecatonicosoctaexon (Catz)
34 80px 80px 80px 80px 80px 80px
t0,2,4{3,3,3,3,3,4}
Stericantellated 7-orthoplex
Cellirhombated hecatonicosoctaexon (Craze)
35 80px 80px 80px 80px 80px 80px
t1,2,4{3,3,3,3,3,4}
Biruncitruncated 7-orthoplex
Biprismatotruncated hecatonicosoctaexon (Baptize)
36 80px 80px 80px 80px 80px
t0,3,4{3,3,3,3,3,4}
Steriruncinated 7-orthoplex
Celliprismated hecatonicosoctaexon (Copaz)
37 80px 80px 80px 80px 80px 80px
t1,3,4{3,3,3,3,3,4}
Biruncicantellated 7-orthoplex
Biprismatorhombated hecatonicosoctaexon (Boparz)
38 80px 80px 80px 80px 80px
t2,3,4{4,3,3,3,3,3}
Tricantitruncated 7-cube
Great trirhombi-hepteractihecatonicosoctaexon (Gotrasaz)
39 80px 80px 80px 80px 80px 80px
t0,1,5{3,3,3,3,3,4}
Pentitruncated 7-orthoplex
Teritruncated hecatonicosoctaexon (Tetaz)
40 80px 80px 80px 80px 80px 80px
t0,2,5{3,3,3,3,3,4}
Penticantellated 7-orthoplex
Terirhombated hecatonicosoctaexon (Teroz)
41 80px 80px 80px 80px 80px 80px
t1,2,5{3,3,3,3,3,4}
Bisteritruncated 7-orthoplex
Bicellitruncated hecatonicosoctaexon (Boctaz)
42 80px 80px 80px 80px 80px 80px
t0,3,5{3,3,3,3,3,4}
Pentiruncinated 7-orthoplex
Teriprismated hecatonicosoctaexon (Topaz)
43 80px 80px 80px 80px 80px 80px
t1,3,5{4,3,3,3,3,3}
Bistericantellated 7-cube
Bicellirhombi-hepteractihecatonicosoctaexon (Bacresaz)
44 80px 80px 80px 80px 80px 80px
t1,3,4{4,3,3,3,3,3}
Biruncicantellated 7-cube
Biprismatorhombated hepteract (Bopresa)
45 80px 80px 80px 80px 80px 80px
t0,4,5{3,3,3,3,3,4}
Pentistericated 7-orthoplex
Tericellated hecatonicosoctaexon (Tocaz)
46 80px 80px 80px 80px 80px 80px
t1,2,5{4,3,3,3,3,3}
Bisteritruncated 7-cube
Bicellitruncated hepteract (Bactasa)
47 80px 80px 80px 80px 80px 80px
t1,2,4{4,3,3,3,3,3}
Biruncitruncated 7-cube
Biprismatotruncated hepteract (Biptesa)
48 80px 80px 80px 80px 80px 80px
t1,2,3{4,3,3,3,3,3}
Bicantitruncated 7-cube
Great birhombated hepteract (Gibrosa)
49 80px 80px 80px 80px 80px 80px
t0,1,6{3,3,3,3,3,4}
Hexitruncated 7-orthoplex
Petitruncated hecatonicosoctaexon (Putaz)
50 80px 80px 80px 80px 80px 80px
t0,2,6{3,3,3,3,3,4}
Hexicantellated 7-orthoplex
Petirhombated hecatonicosoctaexon (Puraz)
51 80px 80px 80px 80px 80px 80px
t0,4,5{4,3,3,3,3,3}
Pentistericated 7-cube
Tericellated hepteract (Tacosa)
52 80px 80px 80px 80px 80px
t0,3,6{4,3,3,3,3,3}
Hexiruncinated 7-cube
Petiprismato-hepteractihecatonicosoctaexon (Pupsez)
53 80px 80px 80px 80px 80px 80px
t0,3,5{4,3,3,3,3,3}
Pentiruncinated 7-cube
Teriprismated hepteract (Tapsa)
54 80px 80px 80px 80px 80px 80px
t0,3,4{4,3,3,3,3,3}
Steriruncinated 7-cube
Celliprismated hepteract (Capsa)
55 80px 80px 80px 80px 80px 80px
t0,2,6{4,3,3,3,3,3}
Hexicantellated 7-cube
Petirhombated hepteract (Purosa)
56 80px 80px 80px 80px 80px 80px
t0,2,5{4,3,3,3,3,3}
Penticantellated 7-cube
Terirhombated hepteract (Tersa)
57 80px 80px 80px 80px 80px 80px
t0,2,4{4,3,3,3,3,3}
Stericantellated 7-cube
Cellirhombated hepteract (Carsa)
58 80px 80px 80px 80px 80px 80px
t0,2,3{4,3,3,3,3,3}
Runcicantellated 7-cube
Prismatorhombated hepteract (Parsa)
59 80px 80px 80px 80px 80px 80px
t0,1,6{4,3,3,3,3,3}
Hexitruncated 7-cube
Petitruncated hepteract (Putsa)
60 80px 80px 80px 80px 80px 80px
t0,1,5{4,3,3,3,3,3}
Pentitruncated 7-cube
Teritruncated hepteract (Tetsa)
61 80px 80px 80px 80px 80px 80px
t0,1,4{4,3,3,3,3,3}
Steritruncated 7-cube
Cellitruncated hepteract (Catsa)
62 80px 80px 80px 80px 80px 80px
t0,1,3{4,3,3,3,3,3}
Runcitruncated 7-cube
Prismatotruncated hepteract (Petsa)
63 80px 80px 80px 80px 80px 80px
t0,1,2{4,3,3,3,3,3}
Cantitruncated 7-cube
Great rhombated hepteract (Gersa)
64 80px 80px 80px 80px 80px
t0,1,2,3{3,3,3,3,3,4}
Runcicantitruncated 7-orthoplex
Great prismated hecatonicosoctaexon (Gopaz)
65 80px 80px 80px 80px 80px 80px
t0,1,2,4{3,3,3,3,3,4}
Stericantitruncated 7-orthoplex
Celligreatorhombated hecatonicosoctaexon (Cogarz)
66 80px 80px 80px 80px 80px 80px
t0,1,3,4{3,3,3,3,3,4}
Steriruncitruncated 7-orthoplex
Celliprismatotruncated hecatonicosoctaexon (Captaz)
67 80px 80px 80px 80px 80px 80px
t0,2,3,4{3,3,3,3,3,4}
Steriruncicantellated 7-orthoplex
Celliprismatorhombated hecatonicosoctaexon (Caparz)
68 80px 80px 80px 80px 80px 80px
t1,2,3,4{3,3,3,3,3,4}
Biruncicantitruncated 7-orthoplex
Great biprismated hecatonicosoctaexon (Gibpaz)
69 80px 80px 80px 80px 80px 80px
t0,1,2,5{3,3,3,3,3,4}
Penticantitruncated 7-orthoplex
Terigreatorhombated hecatonicosoctaexon (Tograz)
70 80px 80px 80px 80px 80px 80px
t0,1,3,5{3,3,3,3,3,4}
Pentiruncitruncated 7-orthoplex
Teriprismatotruncated hecatonicosoctaexon (Toptaz)
71 80px 80px 80px 80px 80px 80px
t0,2,3,5{3,3,3,3,3,4}
Pentiruncicantellated 7-orthoplex
Teriprismatorhombated hecatonicosoctaexon (Toparz)
72 80px 80px 80px 80px 80px 80px
t1,2,3,5{3,3,3,3,3,4}
Bistericantitruncated 7-orthoplex
Bicelligreatorhombated hecatonicosoctaexon (Becogarz)
73 80px 80px 80px 80px 80px 80px
t0,1,4,5{3,3,3,3,3,4}
Pentisteritruncated 7-orthoplex
Tericellitruncated hecatonicosoctaexon (Tacotaz)
74 80px 80px 80px 80px 80px 80px
t0,2,4,5{3,3,3,3,3,4}
Pentistericantellated 7-orthoplex
Tericellirhombated hecatonicosoctaexon (Tocarz)
75 80px 80px 80px 80px 80px 80px
t1,2,4,5{4,3,3,3,3,3}
Bisteriruncitruncated 7-cube
Bicelliprismatotrunki-hepteractihecatonicosoctaexon (Bocaptosaz)
76 80px 80px 80px 80px 80px 80px
t0,3,4,5{3,3,3,3,3,4}
Pentisteriruncinated 7-orthoplex
Tericelliprismated hecatonicosoctaexon (Tecpaz)
77 80px 80px 80px 80px 80px 80px
t1,2,3,5{4,3,3,3,3,3}
Bistericantitruncated 7-cube
Bicelligreatorhombated hepteract (Becgresa)
78 80px 80px 80px 80px 80px 80px
t1,2,3,4{4,3,3,3,3,3}
Biruncicantitruncated 7-cube
Great biprismated hepteract (Gibposa)
79 80px 80px 80px 80px 80px 80px
t0,1,2,6{3,3,3,3,3,4}
Hexicantitruncated 7-orthoplex
Petigreatorhombated hecatonicosoctaexon (Pugarez)
80 80px 80px 80px 80px 80px 80px
t0,1,3,6{3,3,3,3,3,4}
Hexiruncitruncated 7-orthoplex
Petiprismatotruncated hecatonicosoctaexon (Papataz)
81 80px 80px 80px 80px 80px 80px
t0,2,3,6{3,3,3,3,3,4}
Hexiruncicantellated 7-orthoplex
Petiprismatorhombated hecatonicosoctaexon (Puparez)
82 80px 80px 80px 80px 80px 80px
t0,3,4,5{4,3,3,3,3,3}
Pentisteriruncinated 7-cube
Tericelliprismated hepteract (Tecpasa)
83 80px 80px 80px 80px 80px 80px
t0,1,4,6{3,3,3,3,3,4}
Hexisteritruncated 7-orthoplex
Peticellitruncated hecatonicosoctaexon (Pucotaz)
84 80px 80px 80px 80px 80px 80px
t0,2,4,6{4,3,3,3,3,3}
Hexistericantellated 7-cube
Peticellirhombi-hepteractihecatonicosoctaexon (Pucrosaz)
85 80px 80px 80px 80px 80px 80px
t0,2,4,5{4,3,3,3,3,3}
Pentistericantellated 7-cube
Tericellirhombated hepteract (Tecresa)
86 80px 80px 80px 80px 80px 80px
t0,2,3,6{4,3,3,3,3,3}
Hexiruncicantellated 7-cube
Petiprismatorhombated hepteract (Pupresa)
87 80px 80px 80px 80px 80px 80px
t0,2,3,5{4,3,3,3,3,3}
Pentiruncicantellated 7-cube
Teriprismatorhombated hepteract (Topresa)
88 80px 80px 80px 80px 80px 80px
t0,2,3,4{4,3,3,3,3,3}
Steriruncicantellated 7-cube
Celliprismatorhombated hepteract (Copresa)
89 80px 80px 80px 80px 80px 80px
t0,1,5,6{4,3,3,3,3,3}
Hexipentitruncated 7-cube
Petiteritrunki-hepteractihecatonicosoctaexon (Putatosez)
90 80px 80px 80px 80px 80px 80px
t0,1,4,6{4,3,3,3,3,3}
Hexisteritruncated 7-cube
Peticellitruncated hepteract (Pacutsa)
91 80px 80px 80px 80px 80px 80px
t0,1,4,5{4,3,3,3,3,3}
Pentisteritruncated 7-cube
Tericellitruncated hepteract (Tecatsa)
92 80px 80px 80px 80px 80px 80px
t0,1,3,6{4,3,3,3,3,3}
Hexiruncitruncated 7-cube
Petiprismatotruncated hepteract (Pupetsa)
93 80px 80px 80px 80px 80px 80px
t0,1,3,5{4,3,3,3,3,3}
Pentiruncitruncated 7-cube
Teriprismatotruncated hepteract (Toptosa)
94 80px 80px 80px 80px 80px 80px
t0,1,3,4{4,3,3,3,3,3}
Steriruncitruncated 7-cube
Celliprismatotruncated hepteract (Captesa)
95 80px 80px 80px 80px 80px 80px
t0,1,2,6{4,3,3,3,3,3}
Hexicantitruncated 7-cube
Petigreatorhombated hepteract (Pugrosa)
96 80px 80px 80px 80px 80px 80px
t0,1,2,5{4,3,3,3,3,3}
Penticantitruncated 7-cube
Terigreatorhombated hepteract (Togresa)
97 80px 80px 80px 80px 80px 80px
t0,1,2,4{4,3,3,3,3,3}
Stericantitruncated 7-cube
Celligreatorhombated hepteract (Cogarsa)
98 80px 80px 80px 80px 80px 80px
t0,1,2,3{4,3,3,3,3,3}
Runcicantitruncated 7-cube
Great prismated hepteract (Gapsa)
99 80px 80px 80px 80px 80px 80px
t0,1,2,3,4{3,3,3,3,3,4}
Steriruncicantitruncated 7-orthoplex
Great cellated hecatonicosoctaexon (Gocaz)
100 80px 80px 80px 80px 80px
t0,1,2,3,5{3,3,3,3,3,4}
Pentiruncicantitruncated 7-orthoplex
Terigreatoprismated hecatonicosoctaexon (Tegopaz)
101 80px 80px 80px 80px 80px
t0,1,2,4,5{3,3,3,3,3,4}
Pentistericantitruncated 7-orthoplex
Tericelligreatorhombated hecatonicosoctaexon (Tecagraz)
102 80px 80px 80px 80px 80px
t0,1,3,4,5{3,3,3,3,3,4}
Pentisteriruncitruncated 7-orthoplex
Tericelliprismatotruncated hecatonicosoctaexon (Tecpotaz)
103 80px 80px 80px 80px 80px
t0,2,3,4,5{3,3,3,3,3,4}
Pentisteriruncicantellated 7-orthoplex
Tericelliprismatorhombated hecatonicosoctaexon (Tacparez)
104 80px 80px 80px 80px 80px
t1,2,3,4,5{4,3,3,3,3,3}
Bisteriruncicantitruncated 7-cube
Great bicelli-hepteractihecatonicosoctaexon (Gabcosaz)
105 80px 80px 80px 80px 80px 80px
t0,1,2,3,6{3,3,3,3,3,4}
Hexiruncicantitruncated 7-orthoplex
Petigreatoprismated hecatonicosoctaexon (Pugopaz)
106 80px 80px 80px 80px 80px
t0,1,2,4,6{3,3,3,3,3,4}
Hexistericantitruncated 7-orthoplex
Peticelligreatorhombated hecatonicosoctaexon (Pucagraz)
107 80px 80px 80px 80px 80px
t0,1,3,4,6{3,3,3,3,3,4}
Hexisteriruncitruncated 7-orthoplex
Peticelliprismatotruncated hecatonicosoctaexon (Pucpotaz)
108 80px 80px 80px 80px 80px
t0,2,3,4,6{4,3,3,3,3,3}
Hexisteriruncicantellated 7-cube
Peticelliprismatorhombi-hepteractihecatonicosoctaexon (Pucprosaz)
109 80px 80px 80px 80px 80px
t0,2,3,4,5{4,3,3,3,3,3}
Pentisteriruncicantellated 7-cube
Tericelliprismatorhombated hepteract (Tocpresa)
110 80px 80px 80px 80px 80px 80px
t0,1,2,5,6{3,3,3,3,3,4}
Hexipenticantitruncated 7-orthoplex
Petiterigreatorhombated hecatonicosoctaexon (Putegraz)
111 80px 80px 80px 80px 80px
t0,1,3,5,6{4,3,3,3,3,3}
Hexipentiruncitruncated 7-cube
Petiteriprismatotrunki-hepteractihecatonicosoctaexon (Putpetsaz)
112 80px 80px 80px 80px 80px
t0,1,3,4,6{4,3,3,3,3,3}
Hexisteriruncitruncated 7-cube
Peticelliprismatotruncated hepteract (Pucpetsa)
113 80px 80px 80px 80px 80px
t0,1,3,4,5{4,3,3,3,3,3}
Pentisteriruncitruncated 7-cube
Tericelliprismatotruncated hepteract (Tecpetsa)
114 80px 80px 80px 80px 80px 80px
t0,1,2,5,6{4,3,3,3,3,3}
Hexipenticantitruncated 7-cube
Petiterigreatorhombated hepteract (Putgresa)
115 80px 80px 80px 80px 80px
t0,1,2,4,6{4,3,3,3,3,3}
Hexistericantitruncated 7-cube
Peticelligreatorhombated hepteract (Pucagrosa)
116 80px 80px 80px 80px 80px
t0,1,2,4,5{4,3,3,3,3,3}
Pentistericantitruncated 7-cube
Tericelligreatorhombated hepteract (Tecgresa)
117 80px 80px 80px 80px
t0,1,2,3,6{4,3,3,3,3,3}
Hexiruncicantitruncated 7-cube
Petigreatoprismated hepteract (Pugopsa)
118 80px 80px 80px
t0,1,2,3,5{4,3,3,3,3,3}
Pentiruncicantitruncated 7-cube
Terigreatoprismated hepteract (Togapsa)
119 80px 80px 80px 80px
t0,1,2,3,4{4,3,3,3,3,3}
Steriruncicantitruncated 7-cube
Great cellated hepteract (Gacosa)
120 80px 80px 80px 80px 80px
t0,1,2,3,4,5{3,3,3,3,3,4}
Pentisteriruncicantitruncated 7-orthoplex
Great terated hecatonicosoctaexon (Gotaz)
121 80px 80px 80px 80px
t0,1,2,3,4,6{3,3,3,3,3,4}
Hexisteriruncicantitruncated 7-orthoplex
Petigreatocellated hecatonicosoctaexon (Pugacaz)
122 80px 80px 80px 80px 80px
t0,1,2,3,5,6{3,3,3,3,3,4}
Hexipentiruncicantitruncated 7-orthoplex
Petiterigreatoprismated hecatonicosoctaexon (Putgapaz)
123 80px 80px 80px 80px 80px
t0,1,2,4,5,6{4,3,3,3,3,3}
Hexipentistericantitruncated 7-cube
Petitericelligreatorhombi-hepteractihecatonicosoctaexon (Putcagrasaz)
124 80px 80px 80px 80px 80px
t0,1,2,3,5,6{4,3,3,3,3,3}
Hexipentiruncicantitruncated 7-cube
Petiterigreatoprismated hepteract (Putgapsa)
125 80px 80px 80px 80px 80px
t0,1,2,3,4,6{4,3,3,3,3,3}
Hexisteriruncicantitruncated 7-cube
Petigreatocellated hepteract (Pugacasa)
126 80px 80px 80px 80px 80px
t0,1,2,3,4,5{4,3,3,3,3,3}
Pentisteriruncicantitruncated 7-cube
Great terated hepteract (Gotesa)
127 80px 80px 80px 80px 80px
t0,1,2,3,4,5,6{4,3,3,3,3,3}
Omnitruncated 7-cube
Great peti-hepteractihecatonicosoctaexon (Guposaz)

## References

• H.S.M. Coxeter:
• H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
• Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN:978-0-471-01003-6 [1]
• (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10]
• (Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
• (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
• N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. Dissertation, University of Toronto, 1966
•
Notes
Fundamental convex regular and uniform polytopes in dimensions 2–10
Family An Bn I2(p) / Dn E6 / E7 / E8 / F4 / G2 Hn
Regular polygon Triangle Square p-gon Hexagon Pentagon
Uniform polyhedron Tetrahedron OctahedronCube Demicube DodecahedronIcosahedron
Uniform 4-polytope 5-cell 16-cellTesseract Demitesseract 24-cell 120-cell600-cell
Uniform 5-polytope 5-simplex 5-orthoplex5-cube 5-demicube
Uniform 6-polytope 6-simplex 6-orthoplex6-cube 6-demicube 122221
Uniform 7-polytope 7-simplex 7-orthoplex7-cube 7-demicube 132231321
Uniform 8-polytope 8-simplex 8-orthoplex8-cube 8-demicube 142241421
Uniform 9-polytope 9-simplex 9-orthoplex9-cube 9-demicube
Uniform 10-polytope 10-simplex 10-orthoplex10-cube 10-demicube
Uniform n-polytope n-simplex n-orthoplexn-cube n-demicube 1k22k1k21 n-pentagonal polytope
Topics: Polytope familiesRegular polytopeList of regular polytopes and compounds