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In 6-dimensional geometry, there are 64 uniform polytopes with B6 symmetry. There are two regular forms, the 6-orthoplex, and 6-cube with 12 and 64 vertices respectively. The 6-demicube is added with half the symmetry.

They can be visualized as symmetric orthographic projections in Coxeter planes of the B6 Coxeter group, and other subgroups.

Graphs

Symmetric orthographic projections of these 64 polytopes can be made in the B6, B5, B4, B3, B2, A5, A3, Coxeter planes. Ak has [k+1] symmetry, and Bk has [2k] symmetry.

These 64 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
Names
B6
[12]
B5 / D4 / A4
[10]
B4
[8]
B3 / A2
[6]
B2
[4]
A5
[6]
A3
[4]
1 6-cube t5.svg 6-cube t5 B5.svg 6-cube t5 B4.svg 6-cube t5 B3.svg 6-cube t5 B2.svg 6-cube t5 A5.svg 6-cube t5 A3.svg CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
{3,3,3,3,4}
6-orthoplex
Hexacontatetrapeton (gee)
2 6-cube t4.svg 6-cube t4 B5.svg 6-cube t4 B4.svg 6-cube t4 B3.svg 6-cube t4 B2.svg 6-cube t4 A5.svg 6-cube t4 A3.svg CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t1{3,3,3,3,4}
Rectified 6-orthoplex
Rectified hexacontatetrapeton (rag)
3 6-cube t3.svg 6-cube t3 B5.svg 6-cube t3 B4.svg 6-cube t3 B3.svg 6-cube t3 B2.svg 6-cube t3 A5.svg 6-cube t3 A3.svg CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t2{3,3,3,3,4}
Birectified 6-orthoplex
Birectified hexacontatetrapeton (brag)
4 6-cube t2.svg 6-cube t2 B5.svg 6-cube t2 B4.svg 6-cube t2 B3.svg 6-cube t2 B2.svg 6-cube t2 A5.svg 6-cube t2 A3.svg CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t2{4,3,3,3,3}
Birectified 6-cube
Birectified hexeract (brox)
5 6-cube t1.svg 6-cube t1 B5.svg 6-cube t1 B4.svg 6-cube t1 B3.svg 6-cube t1 B2.svg 6-cube t1 A5.svg 6-cube t1 A3.svg CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t1{4,3,3,3,3}
Rectified 6-cube
Rectified hexeract (rax)
6 6-cube t0.svg 6-cube t0 B5.svg 4-cube t0.svg 6-cube t0 B3.svg 6-cube t0 B2.svg 6-cube t0 A5.svg 6-cube t0 A3.svg CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
{4,3,3,3,3}
6-cube
Hexeract (ax)
64 6-demicube t0 B6.svg 6-demicube t0 D6.svg 6-demicube t0 D5.svg 6-demicube t0 D4.svg 6-demicube t0 D3.svg 6-demicube t0 A5.svg 6-demicube t0 A3.svg CDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
h{4,3,3,3,3}
6-demicube
Hemihexeract
7 6-cube t45.svg 6-cube t45 B5.svg 6-cube t45 B4.svg 6-cube t45 B3.svg 6-cube t45 B2.svg 6-cube t45 A5.svg 6-cube t45 A3.svg CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1{3,3,3,3,4}
Truncated 6-orthoplex
Truncated hexacontatetrapeton (tag)
8 6-cube t35.svg 6-cube t35 B5.svg 6-cube t35 B4.svg 6-cube t35 B3.svg 6-cube t35 B2.svg 6-cube t35 A5.svg 6-cube t35 A3.svg CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,2{3,3,3,3,4}
Cantellated 6-orthoplex
Small rhombated hexacontatetrapeton (srog)
9 6-cube t34.svg 6-cube t34 B5.svg 6-cube t34 B4.svg 6-cube t34 B3.svg 6-cube t34 B2.svg 6-cube t34 A5.svg 6-cube t34 A3.svg CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t1,2{3,3,3,3,4}
Bitruncated 6-orthoplex
Bitruncated hexacontatetrapeton (botag)
10 6-cube t25.svg 6-cube t25 B5.svg 6-cube t25 B4.svg 6-cube t25 B3.svg 6-cube t25 B2.svg 6-cube t25 A5.svg 6-cube t25 A3.svg CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,3{3,3,3,3,4}
Runcinated 6-orthoplex
Small prismated hexacontatetrapeton (spog)
11 6-cube t24.svg 6-cube t24 B5.svg 6-cube t24 B4.svg 6-cube t24 B3.svg 6-cube t24 B2.svg 6-cube t24 A5.svg 6-cube t24 A3.svg CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t1,3{3,3,3,3,4}
Bicantellated 6-orthoplex
Small birhombated hexacontatetrapeton (siborg)
12 6-cube t23.svg 6-cube t23 B5.svg 6-cube t23 B4.svg 6-cube t23 B3.svg 6-cube t23 B2.svg 6-cube t23 A5.svg 6-cube t23 A3.svg CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t2,3{4,3,3,3,3}
Tritruncated 6-cube
Hexeractihexacontitetrapeton (xog)
13 6-cube t15.svg 6-cube t15 B5.svg 6-cube t15 B4.svg 6-cube t15 B3.svg 6-cube t15 B2.svg 6-cube t15 A5.svg 6-cube t15 A3.svg CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,4{3,3,3,3,4}
Stericated 6-orthoplex
Small cellated hexacontatetrapeton (scag)
14 6-cube t14.svg 6-cube t14 B5.svg 6-cube t14 B4.svg 6-cube t14 B3.svg 6-cube t14 B2.svg 6-cube t14 A5.svg 6-cube t14 A3.svg CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t1,4{4,3,3,3,3}
Biruncinated 6-cube
Small biprismato-hexeractihexacontitetrapeton (sobpoxog)
15 6-cube t13.svg 6-cube t13 B5.svg 6-cube t13 B4.svg 6-cube t13 B3.svg 6-cube t13 B2.svg 6-cube t13 A5.svg 6-cube t13 A3.svg CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t1,3{4,3,3,3,3}
Bicantellated 6-cube
Small birhombated hexeract (saborx)
16 6-cube t12.svg 6-cube t12 B5.svg 6-cube t12 B4.svg 6-cube t12 B3.svg 6-cube t12 B2.svg 6-cube t12 A5.svg 6-cube t12 A3.svg CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t1,2{4,3,3,3,3}
Bitruncated 6-cube
Bitruncated hexeract (botox)
17 6-cube t05.svg 6-cube t05 B5.svg 6-cube t05 B4.svg 6-cube t05 B3.svg 6-cube t05 B2.svg 6-cube t05 A5.svg 6-cube t05 A3.svg CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,5{4,3,3,3,3}
Pentellated 6-cube
Small teri-hexeractihexacontitetrapeton (stoxog)
18 6-cube t04.svg 6-cube t04 B5.svg 6-cube t04 B4.svg 6-cube t04 B3.svg 6-cube t04 B2.svg 6-cube t04 A5.svg 6-cube t04 A3.svg CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t0,4{4,3,3,3,3}
Stericated 6-cube
Small cellated hexeract (scox)
19 6-cube t03.svg 6-cube t03 B5.svg 6-cube t03 B4.svg 6-cube t03 B3.svg 6-cube t03 B2.svg 6-cube t03 A5.svg 6-cube t03 A3.svg CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t0,3{4,3,3,3,3}
Runcinated 6-cube
Small prismated hexeract (spox)
20 6-cube t02.svg 6-cube t02 B5.svg 6-cube t02 B4.svg 6-cube t02 B3.svg 6-cube t02 B2.svg 6-cube t02 A5.svg 6-cube t02 A3.svg CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t0,2{4,3,3,3,3}
Cantellated 6-cube
Small rhombated hexeract (srox)
21 6-cube t01.svg 6-cube t01 B5.svg 6-cube t01 B4.svg 6-cube t01 B3.svg 6-cube t01 B2.svg 6-cube t01 A5.svg 6-cube t01 A3.svg CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t0,1{4,3,3,3,3}
Truncated 6-cube
Truncated hexeract (tox)
22 6-cube t345.svg 6-cube t345 B5.svg 6-cube t345 B4.svg 6-cube t345 B3.svg 6-cube t345 B2.svg 6-cube t345 A5.svg 6-cube t345 A3.svg CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,2{3,3,3,3,4}
Cantitruncated 6-orthoplex
Great rhombated hexacontatetrapeton (grog)
23 6-cube t245.svg 6-cube t245 B5.svg 6-cube t245 B4.svg 6-cube t245 B3.svg 6-cube t245 B2.svg 6-cube t245 A5.svg 6-cube t245 A3.svg CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,3{3,3,3,3,4}
Runcitruncated 6-orthoplex
Prismatotruncated hexacontatetrapeton (potag)
24 6-cube t235.svg 6-cube t235 B5.svg 6-cube t235 B4.svg 6-cube t235 B3.svg 6-cube t235 B2.svg 6-cube t235 A5.svg 6-cube t235 A3.svg CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,2,3{3,3,3,3,4}
Runcicantellated 6-orthoplex
Prismatorhombated hexacontatetrapeton (prog)
25 6-cube t234.svg 6-cube t234 B5.svg 6-cube t234 B4.svg 6-cube t234 B3.svg 6-cube t234 B2.svg 6-cube t234 A5.svg 6-cube t234 A3.svg CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t1,2,3{3,3,3,3,4}
Bicantitruncated 6-orthoplex
Great birhombated hexacontatetrapeton (gaborg)
26 6-cube t145.svg 6-cube t145 B5.svg 6-cube t145 B4.svg 6-cube t145 B3.svg 6-cube t145 B2.svg 6-cube t145 A5.svg 6-cube t145 A3.svg CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,4{3,3,3,3,4}
Steritruncated 6-orthoplex
Cellitruncated hexacontatetrapeton (catog)
27 6-cube t135.svg 6-cube t135 B5.svg 6-cube t135 B4.svg 6-cube t135 B3.svg 6-cube t135 B2.svg 6-cube t135 A5.svg 6-cube t135 A3.svg CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,2,4{3,3,3,3,4}
Stericantellated 6-orthoplex
Cellirhombated hexacontatetrapeton (crag)
28 6-cube t134.svg 6-cube t134 B5.svg 6-cube t134 B4.svg 6-cube t134 B3.svg 6-cube t134 B2.svg 6-cube t134 A5.svg 6-cube t134 A3.svg CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t1,2,4{3,3,3,3,4}
Biruncitruncated 6-orthoplex
Biprismatotruncated hexacontatetrapeton (boprax)
29 6-cube t125.svg 6-cube t125 B5.svg 6-cube t125 B4.svg 6-cube t125 B3.svg 6-cube t125 B2.svg 6-cube t125 A5.svg 6-cube t125 A3.svg CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,3,4{3,3,3,3,4}
Steriruncinated 6-orthoplex
Celliprismated hexacontatetrapeton (copog)
30 6-cube t124.svg 6-cube t124 B5.svg 6-cube t124 B4.svg 6-cube t124 B3.svg 6-cube t124 B2.svg 6-cube t124 A5.svg 6-cube t124 A3.svg CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t1,2,4{4,3,3,3,3}
Biruncitruncated 6-cube
Biprismatotruncated hexeract (boprag)
31 6-cube t123.svg 6-cube t123 B5.svg 6-cube t123 B4.svg 6-cube t123 B3.svg 6-cube t123 B2.svg 6-cube t123 A5.svg 6-cube t123 A3.svg CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t1,2,3{4,3,3,3,3}
Bicantitruncated 6-cube
Great birhombated hexeract (gaborx)
32 6-cube t045.svg 6-cube t045 B5.svg 6-cube t045 B4.svg 6-cube t045 B3.svg 6-cube t045 B2.svg 6-cube t045 A5.svg 6-cube t045 A3.svg CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,5{3,3,3,3,4}
Pentitruncated 6-orthoplex
Teritruncated hexacontatetrapeton (tacox)
33 6-cube t035.svg 6-cube t035 B5.svg 6-cube t035 B4.svg 6-cube t035 B3.svg 6-cube t035 B2.svg 6-cube t035 A5.svg 6-cube t035 A3.svg CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,2,5{3,3,3,3,4}
Penticantellated 6-orthoplex
Terirhombated hexacontatetrapeton (tapox)
34 6-cube t034.svg 6-cube t034 B5.svg 6-cube t034 B4.svg 6-cube t034 B3.svg 6-cube t034 B2.svg 6-cube t034 A5.svg 6-cube t034 A3.svg CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t0,3,4{4,3,3,3,3}
Steriruncinated 6-cube
Celliprismated hexeract (copox)
35 6-cube t025.svg 6-cube t025 B5.svg 6-cube t025 B4.svg 6-cube t025 B3.svg 6-cube t025 B2.svg 6-cube t025 A5.svg 6-cube t025 A3.svg CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,2,5{4,3,3,3,3}
Penticantellated 6-cube
Terirhombated hexeract (topag)
36 6-cube t024.svg 6-cube t024 B5.svg 6-cube t024 B4.svg 6-cube t024 B3.svg 6-cube t024 B2.svg 6-cube t024 A5.svg 6-cube t024 A3.svg CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t0,2,4{4,3,3,3,3}
Stericantellated 6-cube
Cellirhombated hexeract (crax)
37 6-cube t023.svg 6-cube t023 B5.svg 6-cube t023 B4.svg 6-cube t023 B3.svg 6-cube t023 B2.svg 6-cube t023 A5.svg 6-cube t023 A3.svg CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t0,2,3{4,3,3,3,3}
Runcicantellated 6-cube
Prismatorhombated hexeract (prox)
38 6-cube t015.svg 6-cube t015 B5.svg 6-cube t015 B4.svg 6-cube t015 B3.svg 6-cube t015 B2.svg 6-cube t015 A5.svg 6-cube t015 A3.svg CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,1,5{4,3,3,3,3}
Pentitruncated 6-cube
Teritruncated hexeract (tacog)
39 6-cube t014.svg 6-cube t014 B5.svg 6-cube t014 B4.svg 6-cube t014 B3.svg 6-cube t014 B2.svg 6-cube t014 A5.svg 6-cube t014 A3.svg CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t0,1,4{4,3,3,3,3}
Steritruncated 6-cube
Cellitruncated hexeract (catax)
40 6-cube t013.svg 6-cube t013 B5.svg 6-cube t013 B4.svg 6-cube t013 B3.svg 6-cube t013 B2.svg 6-cube t013 A5.svg 6-cube t013 A3.svg CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t0,1,3{4,3,3,3,3}
Runcitruncated 6-cube
Prismatotruncated hexeract (potax)
41 6-cube t012.svg 6-cube t012 B5.svg 6-cube t012 B4.svg 6-cube t012 B3.svg 6-cube t012 B2.svg 6-cube t012 A5.svg 6-cube t012 A3.svg CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t0,1,2{4,3,3,3,3}
Cantitruncated 6-cube
Great rhombated hexeract (grox)
42 6-cube t2345.svg 6-cube t2345 B5.svg 6-cube t2345 B4.svg 6-cube t2345 B3.svg 6-cube t2345 B2.svg 6-cube t2345 A5.svg 6-cube t2345 A3.svg CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,2,3{3,3,3,3,4}
Runcicantitruncated 6-orthoplex
Great prismated hexacontatetrapeton (gopog)
43 6-cube t1345.svg 6-cube t1345 B5.svg 6-cube t1345 B4.svg 6-cube t1345 B3.svg 6-cube t1345 B2.svg 6-cube t1345 A5.svg 6-cube t1345 A3.svg CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,2,4{3,3,3,3,4}
Stericantitruncated 6-orthoplex
Celligreatorhombated hexacontatetrapeton (cagorg)
44 6-cube t1245.svg 6-cube t1245 B5.svg 6-cube t1245 B4.svg 6-cube t1245 B3.svg 6-cube t1245 B2.svg 6-cube t1245 A5.svg 6-cube t1245 A3.svg CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,3,4{3,3,3,3,4}
Steriruncitruncated 6-orthoplex
Celliprismatotruncated hexacontatetrapeton (captog)
45 6-cube t1235.svg 6-cube t1235 B5.svg 6-cube t1235 B4.svg 6-cube t1235 B3.svg 6-cube t1235 B2.svg 6-cube t1235 A5.svg 6-cube t1235 A3.svg CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,2,3,4{3,3,3,3,4}
Steriruncicantellated 6-orthoplex
Celliprismatorhombated hexacontatetrapeton (coprag)
46 6-cube t1234.svg 6-cube t1234 B5.svg 6-cube t1234 B4.svg 6-cube t1234 B3.svg 6-cube t1234 B2.svg 6-cube t1234 A5.svg 6-cube t1234 A3.svg CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t1,2,3,4{4,3,3,3,3}
Biruncicantitruncated 6-cube
Great biprismato-hexeractihexacontitetrapeton (gobpoxog)
47 6-cube t0345.svg 6-cube t0345 B5.svg 6-cube t0345 B4.svg 6-cube t0345 B3.svg 6-cube t0345 B2.svg 6-cube t0345 A5.svg 6-cube t0345 A3.svg CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,2,5{3,3,3,3,4}
Penticantitruncated 6-orthoplex
Terigreatorhombated hexacontatetrapeton (togrig)
48 6-cube t0245.svg 6-cube t0245 B5.svg 6-cube t0245 B4.svg 6-cube t0245 B3.svg 6-cube t0245 B2.svg 6-cube t0245 A5.svg 6-cube t0245 A3.svg CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,3,5{3,3,3,3,4}
Pentiruncitruncated 6-orthoplex
Teriprismatotruncated hexacontatetrapeton (tocrax)
49 6-cube t0235.svg 6-cube t0235 B5.svg 6-cube t0235 B4.svg 6-cube t0235 B3.svg 6-cube t0235 B2.svg 6-cube t0235 A5.svg 6-cube t0235 A3.svg CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,2,3,5{4,3,3,3,3}
Pentiruncicantellated 6-cube
Teriprismatorhombi-hexeractihexacontitetrapeton (tiprixog)
50 6-cube t0234.svg 6-cube t0234 B5.svg 6-cube t0234 B4.svg 6-cube t0234 B3.svg 6-cube t0234 B2.svg 6-cube t0234 A5.svg 6-cube t0234 A3.svg CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t0,2,3,4{4,3,3,3,3}
Steriruncicantellated 6-cube
Celliprismatorhombated hexeract (coprix)
51 6-cube t0145.svg 6-cube t0145 B5.svg 6-cube t0145 B4.svg 6-cube t0145 B3.svg 6-cube t0145 B2.svg 6-cube t0145 A5.svg 6-cube t0145 A3.svg CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,4,5{4,3,3,3,3}
Pentisteritruncated 6-cube
Tericelli-hexeractihexacontitetrapeton (tactaxog)
52 6-cube t0135.svg 6-cube t0135 B5.svg 6-cube t0135 B4.svg 6-cube t0135 B3.svg 6-cube t0135 B2.svg 6-cube t0135 A5.svg 6-cube t0135 A3.svg CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,1,3,5{4,3,3,3,3}
Pentiruncitruncated 6-cube
Teriprismatotruncated hexeract (tocrag)
53 6-cube t0134.svg 6-cube t0134 B5.svg 6-cube t0134 B4.svg 6-cube t0134 B3.svg 6-cube t0134 B2.svg 6-cube t0134 A5.svg 6-cube t0134 A3.svg CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t0,1,3,4{4,3,3,3,3}
Steriruncitruncated 6-cube
Celliprismatotruncated hexeract (captix)
54 6-cube t0125.svg 6-cube t0125 B5.svg 6-cube t0125 B4.svg 6-cube t0125 B3.svg 6-cube t0125 B2.svg 6-cube t0125 A5.svg 6-cube t0125 A3.svg CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,1,2,5{4,3,3,3,3}
Penticantitruncated 6-cube
Terigreatorhombated hexeract (togrix)
55 6-cube t0124.svg 6-cube t0124 B5.svg 6-cube t0124 B4.svg 6-cube t0124 B3.svg 6-cube t0124 B2.svg 6-cube t0124 A5.svg 6-cube t0124 A3.svg CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t0,1,2,4{4,3,3,3,3}
Stericantitruncated 6-cube
Celligreatorhombated hexeract (cagorx)
56 6-cube t0123.svg 6-cube t0123 B5.svg 6-cube t0123 B4.svg 6-cube t0123 B3.svg 6-cube t0123 B2.svg 6-cube t0123 A5.svg 6-cube t0123 A3.svg CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t0,1,2,3{4,3,3,3,3}
Runcicantitruncated 6-cube
Great prismated hexeract (gippox)
57 6-cube t12345.svg 6-cube t12345 B5.svg 6-cube t12345 B4.svg 6-cube t12345 B3.svg 6-cube t12345 B2.svg 6-cube t12345 A5.svg 6-cube t12345 A3.svg CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,2,3,4{3,3,3,3,4}
Steriruncicantitruncated 6-orthoplex
Great cellated hexacontatetrapeton (gocog)
58 6-cube t02345.svg 6-cube t02345 B5.svg 6-cube t02345 B4.svg 6-cube t02345 B3.svg 6-cube t02345 B2.svg 6-cube t02345 A5.svg 6-cube t02345 A3.svg CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,2,3,5{3,3,3,3,4}
Pentiruncicantitruncated 6-orthoplex
Terigreatoprismated hexacontatetrapeton (tagpog)
59 6-cube t01345.svg 6-cube t01345 B5.svg 6-cube t01345 B4.svg 6-cube t01345 B3.svg 6-cube t01345 B2.svg 6-cube t01345 A5.svg 6-cube t01345 A3.svg CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,2,4,5{3,3,3,3,4}
Pentistericantitruncated 6-orthoplex
Tericelligreatorhombated hexacontatetrapeton (tecagorg)
60 6-cube t01245.svg 6-cube t01245 B5.svg 6-cube t01245 B4.svg 6-cube t01245 B3.svg 6-cube t01245 B2.svg 6-cube t01245 A5.svg 6-cube t01245 A3.svg CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,2,4,5{4,3,3,3,3}
Pentistericantitruncated 6-cube
Tericelligreatorhombated hexeract (tocagrax)
61 6-cube t01235.svg 6-cube t01235 B5.svg 6-cube t01235 B4.svg 6-cube t01235 B3.svg 6-cube t01235 B2.svg 6-cube t01235 A5.svg 6-cube t01235 A3.svg CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,1,2,3,5{4,3,3,3,3}
Pentiruncicantitruncated 6-cube
Terigreatoprismated hexeract (tagpox)
62 6-cube t01234.svg 6-cube t01234 B5.svg 6-cube t01234 B4.svg 6-cube t01234 B3.svg 6-cube t01234 B2.svg 6-cube t01234 A5.svg 6-cube t01234 A3.svg CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t0,1,2,3,4{4,3,3,3,3}
Steriruncicantitruncated 6-cube
Great cellated hexeract (gocax)
63 6-cube t012345.svg 6-cube t012345 B5.svg 6-cube t012345 B4.svg 6-cube t012345 B3.svg 6-cube t012345 B2.svg 6-cube t012345 A5.svg 6-cube t012345 A3.svg CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,2,3,4,5{4,3,3,3,3}
Omnitruncated 6-cube
Great teri-hexeractihexacontitetrapeton (gotaxog)

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
Klitzing, Richard. "6D uniform polytopes (polypeta)".

Notes

Wiley::Kaleidoscopes: Selected Writings of H.S.M. Coxeter

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 4-polytope 5-cell 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

Mathematics Encyclopedia

Hellenica World - Scientific Library

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