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B8 polytope

Orthographic projections in the B8 Coxeter plane

8-cube
8-orthoplex
8-demicube

In 8-dimensional geometry, there are 256 uniform polytopes with B8 symmetry. There are two regular forms, the 8-orthoplex and 8-cube, with 16 and 256 vertices respectively. The 8-demicube is added with half the symmetry.

They can be visualized as symmetric orthographic projections in Coxeter planes of the B8 Coxeter group, and other subgroups.

Graphs

Symmetric orthographic projections of these 256 polytopes can be made in the B8, B7, B6, B5, B4, B3, B2, A7, A5, A3, Coxeter planes. Ak has [k+1] symmetry, and Bk has [2k] symmetry.

These 256 polytopes are each shown in these 10 symmetry planes, with vertices and edges drawn, and vertices colored by the number of overlapping vertices in each projective position.

# Element counts Coxeter-Dynkin diagram
Schläfli symbol
Name
B8
[16]		 B7
[14]		 B6
[12]		 B5
[10]		 B4
[8]		 B3
[6]		 B2
[4]		 A7
[8]		 A5
[6]		 A3
[4]
1
t0{3,3,3,3,3,3,4}
8-orthoplex
Diacosipentacontahexazetton (ek)
2
t1{3,3,3,3,3,3,4}
Rectified 8-orthoplex
Rectified diacosipentacontahexazetton (rek)
3
t2{3,3,3,3,3,3,4}
Birectified 8-orthoplex
Birectified diacosipentacontahexazetton (bark)
4
t3{3,3,3,3,3,3,4}
Trirectified 8-orthoplex
Trirectified diacosipentacontahexazetton (tark)
5
t3{4,3,3,3,3,3,3}
Trirectified 8-cube
Trirectified octeract (tro)
6
t2{4,3,3,3,3,3,3}
Birectified 8-cube
Birectified octeract (bro)
7
t1{4,3,3,3,3,3,3}
Rectified 8-cube
Rectified octeract (recto)
8
t0{4,3,3,3,3,3,3}
8-cube
Octeract (octo)
9
t0,1{3,3,3,3,3,3,4}
Truncated 8-orthoplex
Truncated diacosipentacontahexazetton (tek)
10
t0,2{3,3,3,3,3,3,4}
Cantellated 8-orthoplex
Small rhombated diacosipentacontahexazetton (srek)
11
t1,2{3,3,3,3,3,3,4}
Bitruncated 8-orthoplex
Bitruncated diacosipentacontahexazetton (batek)
12
t0,3{3,3,3,3,3,3,4}
Runcinated 8-orthoplex
Small prismated diacosipentacontahexazetton (spek)
13
t1,3{3,3,3,3,3,3,4}
Bicantellated 8-orthoplex
Small birhombated diacosipentacontahexazetton (sabork)
14
t2,3{3,3,3,3,3,3,4}
Tritruncated 8-orthoplex
Tritruncated diacosipentacontahexazetton (tatek)
15
t0,4{3,3,3,3,3,3,4}
Stericated 8-orthoplex
Small cellated diacosipentacontahexazetton (scak)
16
t1,4{3,3,3,3,3,3,4}
Biruncinated 8-orthoplex
Small biprismated diacosipentacontahexazetton (sabpek)
17
t2,4{3,3,3,3,3,3,4}
Tricantellated 8-orthoplex
Small trirhombated diacosipentacontahexazetton (satrek)
18
t3,4{4,3,3,3,3,3,3}
Quadritruncated 8-cube
Octeractidiacosipentacontahexazetton (oke)
19
t0,5{3,3,3,3,3,3,4}
Pentellated 8-orthoplex
Small terated diacosipentacontahexazetton (setek)
20
t1,5{3,3,3,3,3,3,4}
Bistericated 8-orthoplex
Small bicellated diacosipentacontahexazetton (sibcak)
21
t2,5{4,3,3,3,3,3,3}
Triruncinated 8-cube
Small triprismato-octeractidiacosipentacontahexazetton (sitpoke)
22
t2,4{4,3,3,3,3,3,3}
Tricantellated 8-cube
Small trirhombated octeract (satro)
23
t2,3{4,3,3,3,3,3,3}
Tritruncated 8-cube
Tritruncated octeract (tato)
24
t0,6{3,3,3,3,3,3,4}
Hexicated 8-orthoplex
Small petated diacosipentacontahexazetton (supek)
25
t1,6{4,3,3,3,3,3,3}
Bipentellated 8-cube
Small biteri-octeractidiacosipentacontahexazetton (sabtoke)
26
t1,5{4,3,3,3,3,3,3}
Bistericated 8-cube
Small bicellated octeract (sobco)
27
t1,4{4,3,3,3,3,3,3}
Biruncinated 8-cube
Small biprismated octeract (sabepo)
28
t1,3{4,3,3,3,3,3,3}
Bicantellated 8-cube
Small birhombated octeract (subro)
29
t1,2{4,3,3,3,3,3,3}
Bitruncated 8-cube
Bitruncated octeract (bato)
30
t0,7{4,3,3,3,3,3,3}
Heptellated 8-cube
Small exi-octeractidiacosipentacontahexazetton (saxoke)
31
t0,6{4,3,3,3,3,3,3}
Hexicated 8-cube
Small petated octeract (supo)
32
t0,5{4,3,3,3,3,3,3}
Pentellated 8-cube
Small terated octeract (soto)
33
t0,4{4,3,3,3,3,3,3}
Stericated 8-cube
Small cellated octeract (soco)
34
t0,3{4,3,3,3,3,3,3}
Runcinated 8-cube
Small prismated octeract (sopo)
35
t0,2{4,3,3,3,3,3,3}
Cantellated 8-cube
Small rhombated octeract (soro)
36
t0,1{4,3,3,3,3,3,3}
Truncated 8-cube
Truncated octeract (tocto)
37
t0,1,2{3,3,3,3,3,3,4}
Cantitruncated 8-orthoplex
Great rhombated diacosipentacontahexazetton
38
t0,1,3{3,3,3,3,3,3,4}
Runcitruncated 8-orthoplex
Prismatotruncated diacosipentacontahexazetton
39
t0,2,3{3,3,3,3,3,3,4}
Runcicantellated 8-orthoplex
Prismatorhombated diacosipentacontahexazetton
40
t1,2,3{3,3,3,3,3,3,4}
Bicantitruncated 8-orthoplex
Great birhombated diacosipentacontahexazetton
41
t0,1,4{3,3,3,3,3,3,4}
Steritruncated 8-orthoplex
Cellitruncated diacosipentacontahexazetton
42
t0,2,4{3,3,3,3,3,3,4}
Stericantellated 8-orthoplex
Cellirhombated diacosipentacontahexazetton
43
t1,2,4{3,3,3,3,3,3,4}
Biruncitruncated 8-orthoplex
Biprismatotruncated diacosipentacontahexazetton
44
t0,3,4{3,3,3,3,3,3,4}
Steriruncinated 8-orthoplex
Celliprismated diacosipentacontahexazetton
45
t1,3,4{3,3,3,3,3,3,4}
Biruncicantellated 8-orthoplex
Biprismatorhombated diacosipentacontahexazetton
46
t2,3,4{3,3,3,3,3,3,4}
Tricantitruncated 8-orthoplex
Great trirhombated diacosipentacontahexazetton
47
t0,1,5{3,3,3,3,3,3,4}
Pentitruncated 8-orthoplex
Teritruncated diacosipentacontahexazetton
48
t0,2,5{3,3,3,3,3,3,4}
Penticantellated 8-orthoplex
Terirhombated diacosipentacontahexazetton
49
t1,2,5{3,3,3,3,3,3,4}
Bisteritruncated 8-orthoplex
Bicellitruncated diacosipentacontahexazetton
50
t0,3,5{3,3,3,3,3,3,4}
Pentiruncinated 8-orthoplex
Teriprismated diacosipentacontahexazetton
51
t1,3,5{3,3,3,3,3,3,4}
Bistericantellated 8-orthoplex
Bicellirhombated diacosipentacontahexazetton
52
t2,3,5{3,3,3,3,3,3,4}
Triruncitruncated 8-orthoplex
Triprismatotruncated diacosipentacontahexazetton
53
t0,4,5{3,3,3,3,3,3,4}
Pentistericated 8-orthoplex
Tericellated diacosipentacontahexazetton
54
t1,4,5{3,3,3,3,3,3,4}
Bisteriruncinated 8-orthoplex
Bicelliprismated diacosipentacontahexazetton
55
t2,3,5{4,3,3,3,3,3,3}
Triruncitruncated 8-cube
Triprismatotruncated octeract
56
t2,3,4{4,3,3,3,3,3,3}
Tricantitruncated 8-cube
Great trirhombated octeract
57
t0,1,6{3,3,3,3,3,3,4}
Hexitruncated 8-orthoplex
Petitruncated diacosipentacontahexazetton
58
t0,2,6{3,3,3,3,3,3,4}
Hexicantellated 8-orthoplex
Petirhombated diacosipentacontahexazetton
59
t1,2,6{3,3,3,3,3,3,4}
Bipentitruncated 8-orthoplex
Biteritruncated diacosipentacontahexazetton
60
t0,3,6{3,3,3,3,3,3,4}
Hexiruncinated 8-orthoplex
Petiprismated diacosipentacontahexazetton
61
t1,3,6{3,3,3,3,3,3,4}
Bipenticantellated 8-orthoplex
Biterirhombated diacosipentacontahexazetton
62
t1,4,5{4,3,3,3,3,3,3}
Bisteriruncinated 8-cube
Bicelliprismated octeract
63
t0,4,6{3,3,3,3,3,3,4}
Hexistericated 8-orthoplex
Peticellated diacosipentacontahexazetton
64
t1,3,6{4,3,3,3,3,3,3}
Bipenticantellated 8-cube
Biterirhombated octeract
65
t1,3,5{4,3,3,3,3,3,3}
Bistericantellated 8-cube
Bicellirhombated octeract
66
t1,3,4{4,3,3,3,3,3,3}
Biruncicantellated 8-cube
Biprismatorhombated octeract
67
t0,5,6{3,3,3,3,3,3,4}
Hexipentellated 8-orthoplex
Petiterated diacosipentacontahexazetton
68
t1,2,6{4,3,3,3,3,3,3}
Bipentitruncated 8-cube
Biteritruncated octeract
69
t1,2,5{4,3,3,3,3,3,3}
Bisteritruncated 8-cube
Bicellitruncated octeract
70
t1,2,4{4,3,3,3,3,3,3}
Biruncitruncated 8-cube
Biprismatotruncated octeract
71
t1,2,3{4,3,3,3,3,3,3}
Bicantitruncated 8-cube
Great birhombated octeract
72
t0,1,7{3,3,3,3,3,3,4}
Heptitruncated 8-orthoplex
Exitruncated diacosipentacontahexazetton
73
t0,2,7{3,3,3,3,3,3,4}
Hepticantellated 8-orthoplex
Exirhombated diacosipentacontahexazetton
74
t0,5,6{4,3,3,3,3,3,3}
Hexipentellated 8-cube
Petiterated octeract
75
t0,3,7{3,3,3,3,3,3,4}
Heptiruncinated 8-orthoplex
Exiprismated diacosipentacontahexazetton
76
t0,4,6{4,3,3,3,3,3,3}
Hexistericated 8-cube
Peticellated octeract
77
t0,4,5{4,3,3,3,3,3,3}
Pentistericated 8-cube
Tericellated octeract
78
t0,3,7{4,3,3,3,3,3,3}
Heptiruncinated 8-cube
Exiprismated octeract
79
t0,3,6{4,3,3,3,3,3,3}
Hexiruncinated 8-cube
Petiprismated octeract
80
t0,3,5{4,3,3,3,3,3,3}
Pentiruncinated 8-cube
Teriprismated octeract
81
t0,3,4{4,3,3,3,3,3,3}
Steriruncinated 8-cube
Celliprismated octeract
82
t0,2,7{4,3,3,3,3,3,3}
Hepticantellated 8-cube
Exirhombated octeract
83
t0,2,6{4,3,3,3,3,3,3}
Hexicantellated 8-cube
Petirhombated octeract
84
t0,2,5{4,3,3,3,3,3,3}
Penticantellated 8-cube
Terirhombated octeract
85
t0,2,4{4,3,3,3,3,3,3}
Stericantellated 8-cube
Cellirhombated octeract
86
t0,2,3{4,3,3,3,3,3,3}
Runcicantellated 8-cube
Prismatorhombated octeract
87
t0,1,7{4,3,3,3,3,3,3}
Heptitruncated 8-cube
Exitruncated octeract
88
t0,1,6{4,3,3,3,3,3,3}
Hexitruncated 8-cube
Petitruncated octeract
89
t0,1,5{4,3,3,3,3,3,3}
Pentitruncated 8-cube
Teritruncated octeract
90
t0,1,4{4,3,3,3,3,3,3}
Steritruncated 8-cube
Cellitruncated octeract
91
t0,1,3{4,3,3,3,3,3,3}
Runcitruncated 8-cube
Prismatotruncated octeract
92
t0,1,2{4,3,3,3,3,3,3}
Cantitruncated 8-cube
Great rhombated octeract
93
t0,1,2,3{3,3,3,3,3,3,4}
Runcicantitruncated 8-orthoplex
Great prismated diacosipentacontahexazetton
94
t0,1,2,4{3,3,3,3,3,3,4}
Stericantitruncated 8-orthoplex
Celligreatorhombated diacosipentacontahexazetton
95
t0,1,3,4{3,3,3,3,3,3,4}
Steriruncitruncated 8-orthoplex
Celliprismatotruncated diacosipentacontahexazetton
96
t0,2,3,4{3,3,3,3,3,3,4}
Steriruncicantellated 8-orthoplex
Celliprismatorhombated diacosipentacontahexazetton
97
t1,2,3,4{3,3,3,3,3,3,4}
Biruncicantitruncated 8-orthoplex
Great biprismated diacosipentacontahexazetton
98
t0,1,2,5{3,3,3,3,3,3,4}
Penticantitruncated 8-orthoplex
Terigreatorhombated diacosipentacontahexazetton
99
t0,1,3,5{3,3,3,3,3,3,4}
Pentiruncitruncated 8-orthoplex
Teriprismatotruncated diacosipentacontahexazetton
100
t0,2,3,5{3,3,3,3,3,3,4}
Pentiruncicantellated 8-orthoplex
Teriprismatorhombated diacosipentacontahexazetton
101
t1,2,3,5{3,3,3,3,3,3,4}
Bistericantitruncated 8-orthoplex
Bicelligreatorhombated diacosipentacontahexazetton
102
t0,1,4,5{3,3,3,3,3,3,4}
Pentisteritruncated 8-orthoplex
Tericellitruncated diacosipentacontahexazetton
103
t0,2,4,5{3,3,3,3,3,3,4}
Pentistericantellated 8-orthoplex
Tericellirhombated diacosipentacontahexazetton
104
t1,2,4,5{3,3,3,3,3,3,4}
Bisteriruncitruncated 8-orthoplex
Bicelliprismatotruncated diacosipentacontahexazetton
105
t0,3,4,5{3,3,3,3,3,3,4}
Pentisteriruncinated 8-orthoplex
Tericelliprismated diacosipentacontahexazetton
106
t1,3,4,5{3,3,3,3,3,3,4}
Bisteriruncicantellated 8-orthoplex
Bicelliprismatorhombated diacosipentacontahexazetton
107
t2,3,4,5{4,3,3,3,3,3,3}
Triruncicantitruncated 8-cube
Great triprismato-octeractidiacosipentacontahexazetton
108
t0,1,2,6{3,3,3,3,3,3,4}
Hexicantitruncated 8-orthoplex
Petigreatorhombated diacosipentacontahexazetton
109
t0,1,3,6{3,3,3,3,3,3,4}
Hexiruncitruncated 8-orthoplex
Petiprismatotruncated diacosipentacontahexazetton
110
t0,2,3,6{3,3,3,3,3,3,4}
Hexiruncicantellated 8-orthoplex
Petiprismatorhombated diacosipentacontahexazetton
111
t1,2,3,6{3,3,3,3,3,3,4}
Bipenticantitruncated 8-orthoplex
Biterigreatorhombated diacosipentacontahexazetton
112
t0,1,4,6{3,3,3,3,3,3,4}
Hexisteritruncated 8-orthoplex
Peticellitruncated diacosipentacontahexazetton
113
t0,2,4,6{3,3,3,3,3,3,4}
Hexistericantellated 8-orthoplex
Peticellirhombated diacosipentacontahexazetton
114
t1,2,4,6{3,3,3,3,3,3,4}
Bipentiruncitruncated 8-orthoplex
Biteriprismatotruncated diacosipentacontahexazetton
115
t0,3,4,6{3,3,3,3,3,3,4}
Hexisteriruncinated 8-orthoplex
Peticelliprismated diacosipentacontahexazetton
116
t1,3,4,6{4,3,3,3,3,3,3}
Bipentiruncicantellated 8-cube
Biteriprismatorhombi-octeractidiacosipentacontahexazetton
117
t1,3,4,5{4,3,3,3,3,3,3}
Bisteriruncicantellated 8-cube
Bicelliprismatorhombated octeract
118
t0,1,5,6{3,3,3,3,3,3,4}
Hexipentitruncated 8-orthoplex
Petiteritruncated diacosipentacontahexazetton
119
t0,2,5,6{3,3,3,3,3,3,4}
Hexipenticantellated 8-orthoplex
Petiterirhombated diacosipentacontahexazetton
120
t1,2,5,6{4,3,3,3,3,3,3}
Bipentisteritruncated 8-cube
Bitericellitrunki-octeractidiacosipentacontahexazetton
121
t0,3,5,6{3,3,3,3,3,3,4}
Hexipentiruncinated 8-orthoplex
Petiteriprismated diacosipentacontahexazetton
122
t1,2,4,6{4,3,3,3,3,3,3}
Bipentiruncitruncated 8-cube
Biteriprismatotruncated octeract
123
t1,2,4,5{4,3,3,3,3,3,3}
Bisteriruncitruncated 8-cube
Bicelliprismatotruncated octeract
124
t0,4,5,6{3,3,3,3,3,3,4}
Hexipentistericated 8-orthoplex
Petitericellated diacosipentacontahexazetton
125
t1,2,3,6{4,3,3,3,3,3,3}
Bipenticantitruncated 8-cube
Biterigreatorhombated octeract
126
t1,2,3,5{4,3,3,3,3,3,3}
Bistericantitruncated 8-cube
Bicelligreatorhombated octeract
127
t1,2,3,4{4,3,3,3,3,3,3}
Biruncicantitruncated 8-cube
Great biprismated octeract
128
t0,1,2,7{3,3,3,3,3,3,4}
Hepticantitruncated 8-orthoplex
Exigreatorhombated diacosipentacontahexazetton
129
t0,1,3,7{3,3,3,3,3,3,4}
Heptiruncitruncated 8-orthoplex
Exiprismatotruncated diacosipentacontahexazetton
130
t0,2,3,7{3,3,3,3,3,3,4}
Heptiruncicantellated 8-orthoplex
Exiprismatorhombated diacosipentacontahexazetton
131
t0,4,5,6{4,3,3,3,3,3,3}
Hexipentistericated 8-cube
Petitericellated octeract
132
t0,1,4,7{3,3,3,3,3,3,4}
Heptisteritruncated 8-orthoplex
Exicellitruncated diacosipentacontahexazetton
133
t0,2,4,7{3,3,3,3,3,3,4}
Heptistericantellated 8-orthoplex
Exicellirhombated diacosipentacontahexazetton
134
t0,3,5,6{4,3,3,3,3,3,3}
Hexipentiruncinated 8-cube
Petiteriprismated octeract
135
t0,3,4,7{4,3,3,3,3,3,3}
Heptisteriruncinated 8-cube
Exicelliprismato-octeractidiacosipentacontahexazetton
136
t0,3,4,6{4,3,3,3,3,3,3}
Hexisteriruncinated 8-cube
Peticelliprismated octeract
137
t0,3,4,5{4,3,3,3,3,3,3}
Pentisteriruncinated 8-cube
Tericelliprismated octeract
138
t0,1,5,7{3,3,3,3,3,3,4}
Heptipentitruncated 8-orthoplex
Exiteritruncated diacosipentacontahexazetton
139
t0,2,5,7{4,3,3,3,3,3,3}
Heptipenticantellated 8-cube
Exiterirhombi-octeractidiacosipentacontahexazetton
140
t0,2,5,6{4,3,3,3,3,3,3}
Hexipenticantellated 8-cube
Petiterirhombated octeract
141
t0,2,4,7{4,3,3,3,3,3,3}
Heptistericantellated 8-cube
Exicellirhombated octeract
142
t0,2,4,6{4,3,3,3,3,3,3}
Hexistericantellated 8-cube
Peticellirhombated octeract
143
t0,2,4,5{4,3,3,3,3,3,3}
Pentistericantellated 8-cube
Tericellirhombated octeract
144
t0,2,3,7{4,3,3,3,3,3,3}
Heptiruncicantellated 8-cube
Exiprismatorhombated octeract
145
t0,2,3,6{4,3,3,3,3,3,3}
Hexiruncicantellated 8-cube
Petiprismatorhombated octeract
146
t0,2,3,5{4,3,3,3,3,3,3}
Pentiruncicantellated 8-cube
Teriprismatorhombated octeract
147
t0,2,3,4{4,3,3,3,3,3,3}
Steriruncicantellated 8-cube
Celliprismatorhombated octeract
148
t0,1,6,7{4,3,3,3,3,3,3}
Heptihexitruncated 8-cube
Exipetitrunki-octeractidiacosipentacontahexazetton
149
t0,1,5,7{4,3,3,3,3,3,3}
Heptipentitruncated 8-cube
Exiteritruncated octeract
150
t0,1,5,6{4,3,3,3,3,3,3}
Hexipentitruncated 8-cube
Petiteritruncated octeract
151
t0,1,4,7{4,3,3,3,3,3,3}
Heptisteritruncated 8-cube
Exicellitruncated octeract
152
t0,1,4,6{4,3,3,3,3,3,3}
Hexisteritruncated 8-cube
Peticellitruncated octeract
153
t0,1,4,5{4,3,3,3,3,3,3}
Pentisteritruncated 8-cube
Tericellitruncated octeract
154
t0,1,3,7{4,3,3,3,3,3,3}
Heptiruncitruncated 8-cube
Exiprismatotruncated octeract
155
t0,1,3,6{4,3,3,3,3,3,3}
Hexiruncitruncated 8-cube
Petiprismatotruncated octeract
156
t0,1,3,5{4,3,3,3,3,3,3}
Pentiruncitruncated 8-cube
Teriprismatotruncated octeract
157
t0,1,3,4{4,3,3,3,3,3,3}
Steriruncitruncated 8-cube
Celliprismatotruncated octeract
158
t0,1,2,7{4,3,3,3,3,3,3}
Hepticantitruncated 8-cube
Exigreatorhombated octeract
159
t0,1,2,6{4,3,3,3,3,3,3}
Hexicantitruncated 8-cube
Petigreatorhombated octeract
160
t0,1,2,5{4,3,3,3,3,3,3}
Penticantitruncated 8-cube
Terigreatorhombated octeract
161
t0,1,2,4{4,3,3,3,3,3,3}
Stericantitruncated 8-cube
Celligreatorhombated octeract
162
t0,1,2,3{4,3,3,3,3,3,3}
Runcicantitruncated 8-cube
Great prismated octeract
163
t0,1,2,3,4{3,3,3,3,3,3,4}
Steriruncicantitruncated 8-orthoplex
Great cellated diacosipentacontahexazetton
164
t0,1,2,3,5{3,3,3,3,3,3,4}
Pentiruncicantitruncated 8-orthoplex
Terigreatoprismated diacosipentacontahexazetton
165
t0,1,2,4,5{3,3,3,3,3,3,4}
Pentistericantitruncated 8-orthoplex
Tericelligreatorhombated diacosipentacontahexazetton
166
t0,1,3,4,5{3,3,3,3,3,3,4}
Pentisteriruncitruncated 8-orthoplex
Tericelliprismatotruncated diacosipentacontahexazetton
167
t0,2,3,4,5{3,3,3,3,3,3,4}
Pentisteriruncicantellated 8-orthoplex
Tericelliprismatorhombated diacosipentacontahexazetton
168
t1,2,3,4,5{3,3,3,3,3,3,4}
Bisteriruncicantitruncated 8-orthoplex
Great bicellated diacosipentacontahexazetton
169
t0,1,2,3,6{3,3,3,3,3,3,4}
Hexiruncicantitruncated 8-orthoplex
Petigreatoprismated diacosipentacontahexazetton
170
t0,1,2,4,6{3,3,3,3,3,3,4}
Hexistericantitruncated 8-orthoplex
Peticelligreatorhombated diacosipentacontahexazetton
171
t0,1,3,4,6{3,3,3,3,3,3,4}
Hexisteriruncitruncated 8-orthoplex
Peticelliprismatotruncated diacosipentacontahexazetton
172
t0,2,3,4,6{3,3,3,3,3,3,4}
Hexisteriruncicantellated 8-orthoplex
Peticelliprismatorhombated diacosipentacontahexazetton
173
t1,2,3,4,6{3,3,3,3,3,3,4}
Bipentiruncicantitruncated 8-orthoplex
Biterigreatoprismated diacosipentacontahexazetton
174
t0,1,2,5,6{3,3,3,3,3,3,4}
Hexipenticantitruncated 8-orthoplex
Petiterigreatorhombated diacosipentacontahexazetton
175
t0,1,3,5,6{3,3,3,3,3,3,4}
Hexipentiruncitruncated 8-orthoplex
Petiteriprismatotruncated diacosipentacontahexazetton
176
t0,2,3,5,6{3,3,3,3,3,3,4}
Hexipentiruncicantellated 8-orthoplex
Petiteriprismatorhombated diacosipentacontahexazetton
177
t1,2,3,5,6{3,3,3,3,3,3,4}
Bipentistericantitruncated 8-orthoplex
Bitericelligreatorhombated diacosipentacontahexazetton
178
t0,1,4,5,6{3,3,3,3,3,3,4}
Hexipentisteritruncated 8-orthoplex
Petitericellitruncated diacosipentacontahexazetton
179
t0,2,4,5,6{3,3,3,3,3,3,4}
Hexipentistericantellated 8-orthoplex
Petitericellirhombated diacosipentacontahexazetton
180
t1,2,3,5,6{4,3,3,3,3,3,3}
Bipentistericantitruncated 8-cube
Bitericelligreatorhombated octeract
181
t0,3,4,5,6{3,3,3,3,3,3,4}
Hexipentisteriruncinated 8-orthoplex
Petitericelliprismated diacosipentacontahexazetton
182
t1,2,3,4,6{4,3,3,3,3,3,3}
Bipentiruncicantitruncated 8-cube
Biterigreatoprismated octeract
183
t1,2,3,4,5{4,3,3,3,3,3,3}
Bisteriruncicantitruncated 8-cube
Great bicellated octeract
184
t0,1,2,3,7{3,3,3,3,3,3,4}
Heptiruncicantitruncated 8-orthoplex
Exigreatoprismated diacosipentacontahexazetton
185
t0,1,2,4,7{3,3,3,3,3,3,4}
Heptistericantitruncated 8-orthoplex
Exicelligreatorhombated diacosipentacontahexazetton
186
t0,1,3,4,7{3,3,3,3,3,3,4}
Heptisteriruncitruncated 8-orthoplex
Exicelliprismatotruncated diacosipentacontahexazetton
187
t0,2,3,4,7{3,3,3,3,3,3,4}
Heptisteriruncicantellated 8-orthoplex
Exicelliprismatorhombated diacosipentacontahexazetton
188
t0,3,4,5,6{4,3,3,3,3,3,3}
Hexipentisteriruncinated 8-cube
Petitericelliprismated octeract
189
t0,1,2,5,7{3,3,3,3,3,3,4}
Heptipenticantitruncated 8-orthoplex
Exiterigreatorhombated diacosipentacontahexazetton
190
t0,1,3,5,7{3,3,3,3,3,3,4}
Heptipentiruncitruncated 8-orthoplex
Exiteriprismatotruncated diacosipentacontahexazetton
191
t0,2,3,5,7{3,3,3,3,3,3,4}
Heptipentiruncicantellated 8-orthoplex
Exiteriprismatorhombated diacosipentacontahexazetton
192
t0,2,4,5,6{4,3,3,3,3,3,3}
Hexipentistericantellated 8-cube
Petitericellirhombated octeract
193
t0,1,4,5,7{3,3,3,3,3,3,4}
Heptipentisteritruncated 8-orthoplex
Exitericellitruncated diacosipentacontahexazetton
194
t0,2,3,5,7{4,3,3,3,3,3,3}
Heptipentiruncicantellated 8-cube
Exiteriprismatorhombated octeract
195
t0,2,3,5,6{4,3,3,3,3,3,3}
Hexipentiruncicantellated 8-cube
Petiteriprismatorhombated octeract
196
t0,2,3,4,7{4,3,3,3,3,3,3}
Heptisteriruncicantellated 8-cube
Exicelliprismatorhombated octeract
197
t0,2,3,4,6{4,3,3,3,3,3,3}
Hexisteriruncicantellated 8-cube
Peticelliprismatorhombated octeract
198
t0,2,3,4,5{4,3,3,3,3,3,3}
Pentisteriruncicantellated 8-cube
Tericelliprismatorhombated octeract
199
t0,1,2,6,7{3,3,3,3,3,3,4}
Heptihexicantitruncated 8-orthoplex
Exipetigreatorhombated diacosipentacontahexazetton
200
t0,1,3,6,7{3,3,3,3,3,3,4}
Heptihexiruncitruncated 8-orthoplex
Exipetiprismatotruncated diacosipentacontahexazetton
201
t0,1,4,5,7{4,3,3,3,3,3,3}
Heptipentisteritruncated 8-cube
Exitericellitruncated octeract
202
t0,1,4,5,6{4,3,3,3,3,3,3}
Hexipentisteritruncated 8-cube
Petitericellitruncated octeract
203
t0,1,3,6,7{4,3,3,3,3,3,3}
Heptihexiruncitruncated 8-cube
Exipetiprismatotruncated octeract
204
t0,1,3,5,7{4,3,3,3,3,3,3}
Heptipentiruncitruncated 8-cube
Exiteriprismatotruncated octeract
205
t0,1,3,5,6{4,3,3,3,3,3,3}
Hexipentiruncitruncated 8-cube
Petiteriprismatotruncated octeract
206
t0,1,3,4,7{4,3,3,3,3,3,3}
Heptisteriruncitruncated 8-cube
Exicelliprismatotruncated octeract
207
t0,1,3,4,6{4,3,3,3,3,3,3}
Hexisteriruncitruncated 8-cube
Peticelliprismatotruncated octeract
208
t0,1,3,4,5{4,3,3,3,3,3,3}
Pentisteriruncitruncated 8-cube
Tericelliprismatotruncated octeract
209
t0,1,2,6,7{4,3,3,3,3,3,3}
Heptihexicantitruncated 8-cube
Exipetigreatorhombated octeract
210
t0,1,2,5,7{4,3,3,3,3,3,3}
Heptipenticantitruncated 8-cube
Exiterigreatorhombated octeract
211
t0,1,2,5,6{4,3,3,3,3,3,3}
Hexipenticantitruncated 8-cube
Petiterigreatorhombated octeract
212
t0,1,2,4,7{4,3,3,3,3,3,3}
Heptistericantitruncated 8-cube
Exicelligreatorhombated octeract
213
t0,1,2,4,6{4,3,3,3,3,3,3}
Hexistericantitruncated 8-cube
Peticelligreatorhombated octeract
214
t0,1,2,4,5{4,3,3,3,3,3,3}
Pentistericantitruncated 8-cube
Tericelligreatorhombated octeract
215
t0,1,2,3,7{4,3,3,3,3,3,3}
Heptiruncicantitruncated 8-cube
Exigreatoprismated octeract
216
t0,1,2,3,6{4,3,3,3,3,3,3}
Hexiruncicantitruncated 8-cube
Petigreatoprismated octeract
217
t0,1,2,3,5{4,3,3,3,3,3,3}
Pentiruncicantitruncated 8-cube
Terigreatoprismated octeract
218
t0,1,2,3,4{4,3,3,3,3,3,3}
Steriruncicantitruncated 8-cube
Great cellated octeract
219
t0,1,2,3,4,5{3,3,3,3,3,3,4}
Pentisteriruncicantitruncated 8-orthoplex
Great terated diacosipentacontahexazetton
220
t0,1,2,3,4,6{3,3,3,3,3,3,4}
Hexisteriruncicantitruncated 8-orthoplex
Petigreatocellated diacosipentacontahexazetton
221
t0,1,2,3,5,6{3,3,3,3,3,3,4}
Hexipentiruncicantitruncated 8-orthoplex
Petiterigreatoprismated diacosipentacontahexazetton
222
t0,1,2,4,5,6{3,3,3,3,3,3,4}
Hexipentistericantitruncated 8-orthoplex
Petitericelligreatorhombated diacosipentacontahexazetton
223
t0,1,3,4,5,6{3,3,3,3,3,3,4}
Hexipentisteriruncitruncated 8-orthoplex
Petitericelliprismatotruncated diacosipentacontahexazetton
224
t0,2,3,4,5,6{3,3,3,3,3,3,4}
Hexipentisteriruncicantellated 8-orthoplex
Petitericelliprismatorhombated diacosipentacontahexazetton
225
t1,2,3,4,5,6{4,3,3,3,3,3,3}
Bipentisteriruncicantitruncated 8-cube
Great biteri-octeractidiacosipentacontahexazetton
226
t0,1,2,3,4,7{3,3,3,3,3,3,4}
Heptisteriruncicantitruncated 8-orthoplex
Exigreatocellated diacosipentacontahexazetton
227
t0,1,2,3,5,7{3,3,3,3,3,3,4}
Heptipentiruncicantitruncated 8-orthoplex
Exiterigreatoprismated diacosipentacontahexazetton
228
t0,1,2,4,5,7{3,3,3,3,3,3,4}
Heptipentistericantitruncated 8-orthoplex
Exitericelligreatorhombated diacosipentacontahexazetton
229
t0,1,3,4,5,7{3,3,3,3,3,3,4}
Heptipentisteriruncitruncated 8-orthoplex
Exitericelliprismatotruncated diacosipentacontahexazetton
230
t0,2,3,4,5,7{4,3,3,3,3,3,3}
Heptipentisteriruncicantellated 8-cube
Exitericelliprismatorhombi-octeractidiacosipentacontahexazetton
231
t0,2,3,4,5,6{4,3,3,3,3,3,3}
Hexipentisteriruncicantellated 8-cube
Petitericelliprismatorhombated octeract
232
t0,1,2,3,6,7{3,3,3,3,3,3,4}
Heptihexiruncicantitruncated 8-orthoplex
Exipetigreatoprismated diacosipentacontahexazetton
233
t0,1,2,4,6,7{3,3,3,3,3,3,4}
Heptihexistericantitruncated 8-orthoplex
Exipeticelligreatorhombated diacosipentacontahexazetton
234
t0,1,3,4,6,7{4,3,3,3,3,3,3}
Heptihexisteriruncitruncated 8-cube
Exipeticelliprismatotrunki-octeractidiacosipentacontahexazetton
235
t0,1,3,4,5,7{4,3,3,3,3,3,3}
Heptipentisteriruncitruncated 8-cube
Exitericelliprismatotruncated octeract
236
t0,1,3,4,5,6{4,3,3,3,3,3,3}
Hexipentisteriruncitruncated 8-cube
Petitericelliprismatotruncated octeract
237
t0,1,2,5,6,7{4,3,3,3,3,3,3}
Heptihexipenticantitruncated 8-cube
Exipetiterigreatorhombi-octeractidiacosipentacontahexazetton
238
t0,1,2,4,6,7{4,3,3,3,3,3,3}
Heptihexistericantitruncated 8-cube
Exipeticelligreatorhombated octeract
239
t0,1,2,4,5,7{4,3,3,3,3,3,3}
Heptipentistericantitruncated 8-cube
Exitericelligreatorhombated octeract
240
t0,1,2,4,5,6{4,3,3,3,3,3,3}
Hexipentistericantitruncated 8-cube
Petitericelligreatorhombated octeract
241
t0,1,2,3,6,7{4,3,3,3,3,3,3}
Heptihexiruncicantitruncated 8-cube
Exipetigreatoprismated octeract
242
t0,1,2,3,5,7{4,3,3,3,3,3,3}
Heptipentiruncicantitruncated 8-cube
Exiterigreatoprismated octeract
243
t0,1,2,3,5,6{4,3,3,3,3,3,3}
Hexipentiruncicantitruncated 8-cube
Petiterigreatoprismated octeract
244
t0,1,2,3,4,7{4,3,3,3,3,3,3}
Heptisteriruncicantitruncated 8-cube
Exigreatocellated octeract
245
t0,1,2,3,4,6{4,3,3,3,3,3,3}
Hexisteriruncicantitruncated 8-cube
Petigreatocellated octeract
246
t0,1,2,3,4,5{4,3,3,3,3,3,3}
Pentisteriruncicantitruncated 8-cube
Great terated octeract
247
t0,1,2,3,4,5,6{3,3,3,3,3,3,4}
Hexipentisteriruncicantitruncated 8-orthoplex
Great petated diacosipentacontahexazetton
248
t0,1,2,3,4,5,7{3,3,3,3,3,3,4}
Heptipentisteriruncicantitruncated 8-orthoplex
Exigreatoterated diacosipentacontahexazetton
249
t0,1,2,3,4,6,7{3,3,3,3,3,3,4}
Heptihexisteriruncicantitruncated 8-orthoplex
Exipetigreatocellated diacosipentacontahexazetton
250
t0,1,2,3,5,6,7{3,3,3,3,3,3,4}
Heptihexipentiruncicantitruncated 8-orthoplex
Exipetiterigreatoprismated diacosipentacontahexazetton
251
t0,1,2,3,5,6,7{4,3,3,3,3,3,3}
Heptihexipentiruncicantitruncated 8-cube
Exipetiterigreatoprismated octeract
252
t0,1,2,3,4,6,7{4,3,3,3,3,3,3}
Heptihexisteriruncicantitruncated 8-cube
Exipetigreatocellated octeract
253
t0,1,2,3,4,5,7{4,3,3,3,3,3,3}
Heptipentisteriruncicantitruncated 8-cube
Exigreatoterated octeract
254
t0,1,2,3,4,5,6{4,3,3,3,3,3,3}
Hexipentisteriruncicantitruncated 8-cube
Great petated octeract
255
t0,1,2,3,4,5,6,7{4,3,3,3,3,3,3}
Omnitruncated 8-cube
Great exi-octeractidiacosipentacontahexazetton
256
h0{4,3,3,3,3,3,3}
8-demicube
Hemiocteract

References

  • Klitzing, Richard. "8D uniform polytopes (polyzetta)".

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 Octahedron • Cube Demicube Dodecahedron • Icosahedron
Uniform polychoron Pentachoron 16-cell • Tesseract Demitesseract 24-cell 120-cell • 600-cell
Uniform 5-polytope 5-simplex 5-orthoplex • 5-cube 5-demicube
Uniform 6-polytope 6-simplex 6-orthoplex • 6-cube 6-demicube 122 • 221
Uniform 7-polytope 7-simplex 7-orthoplex • 7-cube 7-demicube 132 • 231 • 321
Uniform 8-polytope 8-simplex 8-orthoplex • 8-cube 8-demicube 142 • 241 • 421
Uniform 9-polytope 9-simplex 9-orthoplex • 9-cube 9-demicube
Uniform 10-polytope 10-simplex 10-orthoplex • 10-cube 10-demicube
Uniform n-polytope n-simplex n-orthoplex • n-cube n-demicube 1k2 • 2k1 • k21 n-pentagonal polytope
Topics: Polytope families • Regular polytope • List of regular polytopes and compounds
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