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B8 polytope

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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

[edit]

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

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

Notes

[edit]
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 polychoron Pentachoron 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