- Art Gallery -

In 7-dimensional geometry, there are 71 uniform polytopes with A7 symmetry. There is one self-dual regular form, the 7-simplex with 8 vertices.

Each can be visualized as symmetric orthographic projections in Coxeter planes of the A7 Coxeter group, and other subgroups.

Graphs

Symmetric orthographic projections of these 71 polytopes can be made in the A7, A6, A5, A4, A3, A2 Coxeter planes. Ak has [k+1] symmetry. For even k and symmetrically ringed-diagrams, symmetry doubles to [2(k+1)].

These 71 polytopes are each shown in these 6 symmetry planes, with vertices and edges drawn, and vertices colored by the number of overlapping vertices in each projective position.

# Coxeter-Dynkin diagram
Schläfli symbol
Johnson name
Ak orthogonal projection graphs
A7
[8]
A6
[7]
A5
[6]
A4
[5]
A3
[4]
A2
[3]
1 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png
t0{3,3,3,3,3,3}
7-simplex
7-simplex t0.svg 7-simplex t0 A6.svg 7-simplex t0 A5.svg 7-simplex t0 A4.svg 7-simplex t0 A3.svg 7-simplex t0 A2.svg
2 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png
t1{3,3,3,3,3,3}
Rectified 7-simplex
7-simplex t1.svg 7-simplex t1 A6.svg 7-simplex t1 A5.svg 7-simplex t1 A4.svg 7-simplex t1 A3.svg 7-simplex t1 A2.svg
3 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png
t2{3,3,3,3,3,3}
Birectified 7-simplex
7-simplex t2.svg 7-simplex t2 A6.svg 7-simplex t2 A5.svg 7-simplex t2 A4.svg 7-simplex t2 A3.svg 7-simplex t2 A2.svg
4 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png
t3{3,3,3,3,3,3}
Trirectified 7-simplex
7-simplex t3.svg 7-simplex t3 A6.svg 7-simplex t3 A5.svg 7-simplex t3 A4.svg 7-simplex t3 A3.svg 7-simplex t3 A2.svg
5 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png
t0,1{3,3,3,3,3,3}
Truncated 7-simplex
7-simplex t01.svg 7-simplex t01 A6.svg 7-simplex t01 A5.svg 7-simplex t01 A4.svg 7-simplex t01 A3.svg 7-simplex t01 A2.svg
6 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png
t0,2{3,3,3,3,3,3}
Cantellated 7-simplex
7-simplex t02.svg 7-simplex t02 A6.svg 7-simplex t02 A5.svg 7-simplex t02 A4.svg 7-simplex t02 A3.svg 7-simplex t02 A2.svg
7 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png
t1,2{3,3,3,3,3,3}
Bitruncated 7-simplex
7-simplex t12.svg 7-simplex t12 A6.svg 7-simplex t12 A5.svg 7-simplex t12 A4.svg 7-simplex t12 A3.svg 7-simplex t12 A2.svg
8 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png
t0,3{3,3,3,3,3,3}
Runcinated 7-simplex
7-simplex t03.svg 7-simplex t03 A6.svg 7-simplex t03 A5.svg 7-simplex t03 A4.svg 7-simplex t03 A3.svg 7-simplex t03 A2.svg
9 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png
t1,3{3,3,3,3,3,3}
Bicantellated 7-simplex
7-simplex t13.svg 7-simplex t13 A6.svg 7-simplex t13 A5.svg 7-simplex t13 A4.svg 7-simplex t13 A3.svg 7-simplex t13 A2.svg
10 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png
t2,3{3,3,3,3,3,3}
Tritruncated 7-simplex
7-simplex t23.svg 7-simplex t23 A6.svg 7-simplex t23 A5.svg 7-simplex t23 A4.svg 7-simplex t23 A3.svg 7-simplex t23 A2.svg
11 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png
t0,4{3,3,3,3,3,3}
Stericated 7-simplex
7-simplex t04.svg 7-simplex t04 A6.svg 7-simplex t04 A5.svg 7-simplex t04 A4.svg 7-simplex t04 A3.svg 7-simplex t04 A2.svg
12 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png
t1,4{3,3,3,3,3,3}
Biruncinated 7-simplex
7-simplex t14.svg 7-simplex t14 A6.svg 7-simplex t14 A5.svg 7-simplex t14 A4.svg 7-simplex t14 A3.svg 7-simplex t14 A2.svg
13 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png
t2,4{3,3,3,3,3,3}
Tricantellated 7-simplex
7-simplex t24.svg 7-simplex t24 A6.svg 7-simplex t24 A5.svg 7-simplex t24 A4.svg 7-simplex t24 A3.svg 7-simplex t24 A2.svg
14 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png
t0,5{3,3,3,3,3,3}
Pentellated 7-simplex
7-simplex t05.svg 7-simplex t05 A6.svg 7-simplex t05 A5.svg 7-simplex t05 A4.svg 7-simplex t05 A3.svg 7-simplex t05 A2.svg
15 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png
t1,5{3,3,3,3,3,3}
Bistericated 7-simplex
7-simplex t15.svg 7-simplex t15 A6.svg 7-simplex t15 A5.svg 7-simplex t15 A4.svg 7-simplex t15 A3.svg 7-simplex t15 A2.svg
16 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png
t0,6{3,3,3,3,3,3}
Hexicated 7-simplex
7-simplex t06.svg 7-simplex t06 A6.svg 7-simplex t06 A5.svg 7-simplex t06 A4.svg 7-simplex t06 A3.svg 7-simplex t06 A2.svg
17 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png
t0,1,2{3,3,3,3,3,3}
Cantitruncated 7-simplex
7-simplex t012.svg 7-simplex t012 A6.svg 7-simplex t012 A5.svg 7-simplex t012 A4.svg 7-simplex t012 A3.svg 7-simplex t012 A2.svg
18 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png
t0,1,3{3,3,3,3,3,3}
Runcitruncated 7-simplex
7-simplex t013.svg 7-simplex t013 A6.svg 7-simplex t013 A5.svg 7-simplex t013 A4.svg 7-simplex t013 A3.svg 7-simplex t013 A2.svg
19 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png
t0,2,3{3,3,3,3,3,3}
Runcicantellated 7-simplex
7-simplex t023.svg 7-simplex t023 A6.svg 7-simplex t023 A5.svg 7-simplex t023 A4.svg 7-simplex t023 A3.svg 7-simplex t023 A2.svg
20 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png
t1,2,3{3,3,3,3,3,3}
Bicantitruncated 7-simplex
7-simplex t123.svg 7-simplex t123 A6.svg 7-simplex t123 A5.svg 7-simplex t123 A4.svg 7-simplex t123 A3.svg 7-simplex t123 A2.svg
21 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png
t0,1,4{3,3,3,3,3,3}
Steritruncated 7-simplex
7-simplex t014.svg 7-simplex t014 A6.svg 7-simplex t014 A5.svg 7-simplex t014 A4.svg 7-simplex t014 A3.svg 7-simplex t014 A2.svg
22 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png
t0,2,4{3,3,3,3,3,3}
Stericantellated 7-simplex
7-simplex t024.svg 7-simplex t024 A6.svg 7-simplex t024 A5.svg 7-simplex t024 A4.svg 7-simplex t024 A3.svg 7-simplex t024 A2.svg
23 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png
t1,2,4{3,3,3,3,3,3}
Biruncitruncated 7-simplex
7-simplex t124.svg 7-simplex t124 A6.svg 7-simplex t124 A5.svg 7-simplex t124 A4.svg 7-simplex t124 A3.svg 7-simplex t124 A2.svg
24 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png
t0,3,4{3,3,3,3,3,3}
Steriruncinated 7-simplex
7-simplex t034.svg 7-simplex t034 A6.svg 7-simplex t034 A5.svg 7-simplex t034 A4.svg 7-simplex t034 A3.svg 7-simplex t034 A2.svg
25 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png
t1,3,4{3,3,3,3,3,3}
Biruncicantellated 7-simplex
7-simplex t134.svg 7-simplex t134 A6.svg 7-simplex t134 A5.svg 7-simplex t134 A4.svg 7-simplex t134 A3.svg 7-simplex t134 A2.svg
26 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.png
t2,3,4{3,3,3,3,3,3}
Tricantitruncated 7-simplex
7-simplex t234.svg 7-simplex t234 A6.svg 7-simplex t234 A5.svg 7-simplex t234 A4.svg 7-simplex t234 A3.svg 7-simplex t234 A2.svg
27 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png
t0,1,5{3,3,3,3,3,3}
Pentitruncated 7-simplex
7-simplex t015.svg 7-simplex t015 A6.svg 7-simplex t015 A5.svg 7-simplex t015 A4.svg 7-simplex t015 A3.svg 7-simplex t015 A2.svg
28 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png
t0,2,5{3,3,3,3,3,3}
Penticantellated 7-simplex
7-simplex t025.svg 7-simplex t025 A6.svg 7-simplex t025 A5.svg 7-simplex t025 A4.svg 7-simplex t025 A3.svg 7-simplex t025 A2.svg
29 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png
t1,2,5{3,3,3,3,3,3}
Bisteritruncated 7-simplex
7-simplex t125.svg 7-simplex t125 A6.svg 7-simplex t125 A5.svg 7-simplex t125 A4.svg 7-simplex t125 A3.svg 7-simplex t125 A2.svg
30 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png
t0,3,5{3,3,3,3,3,3}
Pentiruncinated 7-simplex
7-simplex t035.svg 7-simplex t035 A6.svg 7-simplex t035 A5.svg 7-simplex t035 A4.svg 7-simplex t035 A3.svg 7-simplex t035 A2.svg
31 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png
t1,3,5{3,3,3,3,3,3}
Bistericantellated 7-simplex
7-simplex t135.svg 7-simplex t135 A6.svg 7-simplex t135 A5.svg 7-simplex t135 A4.svg 7-simplex t135 A3.svg 7-simplex t135 A2.svg
32 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png
t0,4,5{3,3,3,3,3,3}
Pentistericated 7-simplex
7-simplex t045.svg 7-simplex t045 A6.svg 7-simplex t045 A5.svg 7-simplex t045 A4.svg 7-simplex t045 A3.svg 7-simplex t045 A2.svg
33 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png
t0,1,6{3,3,3,3,3,3}
Hexitruncated 7-simplex
7-simplex t016.svg 7-simplex t016 A6.svg 7-simplex t016 A5.svg 7-simplex t016 A4.svg 7-simplex t016 A3.svg 7-simplex t016 A2.svg
34 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png
t0,2,6{3,3,3,3,3,3}
Hexicantellated 7-simplex
7-simplex t026.svg 7-simplex t026 A6.svg 7-simplex t026 A5.svg 7-simplex t026 A4.svg 7-simplex t026 A3.svg 7-simplex t026 A2.svg
35 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png
t0,3,6{3,3,3,3,3,3}
Hexiruncinated 7-simplex
7-simplex t036.svg 7-simplex t036 A6.svg 7-simplex t036 A5.svg 7-simplex t036 A4.svg 7-simplex t036 A3.svg 7-simplex t036 A2.svg
36 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png
t0,1,2,3{3,3,3,3,3,3}
Runcicantitruncated 7-simplex
7-simplex t0123.svg 7-simplex t0123 A6.svg 7-simplex t0123 A5.svg 7-simplex t0123 A4.svg 7-simplex t0123 A3.svg 7-simplex t0123 A2.svg
37 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png
t0,1,2,4{3,3,3,3,3,3}
Stericantitruncated 7-simplex
7-simplex t0124.svg 7-simplex t0124 A6.svg 7-simplex t0124 A5.svg 7-simplex t0124 A4.svg 7-simplex t0124 A3.svg 7-simplex t0124 A2.svg
38 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png
t0,1,3,4{3,3,3,3,3,3}
Steriruncitruncated 7-simplex
7-simplex t0134.svg 7-simplex t0134 A6.svg 7-simplex t0134 A5.svg 7-simplex t0134 A4.svg 7-simplex t0134 A3.svg 7-simplex t0134 A2.svg
39 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png
t0,2,3,4{3,3,3,3,3,3}
Steriruncicantellated 7-simplex
7-simplex t0234.svg 7-simplex t0234 A6.svg 7-simplex t0234 A5.svg 7-simplex t0234 A4.svg 7-simplex t0234 A3.svg 7-simplex t0234 A2.svg
40 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png
t1,2,3,4{3,3,3,3,3,3}
Biruncicantitruncated 7-simplex
7-simplex t1234.svg 7-simplex t1234 A6.svg 7-simplex t1234 A5.svg 7-simplex t1234 A4.svg 7-simplex t1234 A3.svg 7-simplex t1234 A2.svg
41 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png
t0,1,2,5{3,3,3,3,3,3}
Penticantitruncated 7-simplex
7-simplex t0125.svg 7-simplex t0125 A6.svg 7-simplex t0125 A5.svg 7-simplex t0125 A4.svg 7-simplex t0125 A3.svg 7-simplex t0125 A2.svg
42 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png
t0,1,3,5{3,3,3,3,3,3}
Pentiruncitruncated 7-simplex
7-simplex t0135.svg 7-simplex t0135 A6.svg 7-simplex t0135 A5.svg 7-simplex t0135 A4.svg 7-simplex t0135 A3.svg 7-simplex t0135 A2.svg
43 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png
t0,2,3,5{3,3,3,3,3,3}
Pentiruncicantellated 7-simplex
7-simplex t0235.svg 7-simplex t0235 A6.svg 7-simplex t0235 A5.svg 7-simplex t0235 A4.svg 7-simplex t0235 A3.svg 7-simplex t0235 A2.svg
44 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png
t1,2,3,5{3,3,3,3,3,3}
Bistericantitruncated 7-simplex
7-simplex t1235.svg 7-simplex t1235 A6.svg 7-simplex t1235 A5.svg 7-simplex t1235 A4.svg 7-simplex t1235 A3.svg 7-simplex t1235 A2.svg
45 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png
t0,1,4,5{3,3,3,3,3,3}
Pentisteritruncated 7-simplex
7-simplex t0145.svg 7-simplex t0145 A6.svg 7-simplex t0145 A5.svg 7-simplex t0145 A4.svg 7-simplex t0145 A3.svg 7-simplex t0145 A2.svg
46 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png
t0,2,4,5{3,3,3,3,3,3}
Pentistericantellated 7-simplex
7-simplex t0245.svg 7-simplex t0245 A6.svg 7-simplex t0245 A5.svg 7-simplex t0245 A4.svg 7-simplex t0245 A3.svg 7-simplex t0245 A2.svg
47 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png
t1,2,4,5{3,3,3,3,3,3}
Bisteriruncitruncated 7-simplex
7-simplex t1245.svg 7-simplex t1245 A6.svg 7-simplex t1245 A5.svg 7-simplex t1245 A4.svg 7-simplex t1245 A3.svg 7-simplex t1245 A2.svg
48 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png
t0,3,4,5{3,3,3,3,3,3}
Pentisteriruncinated 7-simplex
7-simplex t0345.svg 7-simplex t0345 A6.svg 7-simplex t0345 A5.svg 7-simplex t0345 A4.svg 7-simplex t0345 A3.svg 7-simplex t0345 A2.svg
49 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png
t0,1,2,6{3,3,3,3,3,3}
Hexicantitruncated 7-simplex
7-simplex t0126.svg 7-simplex t0126 A6.svg 7-simplex t0126 A5.svg 7-simplex t0126 A4.svg 7-simplex t0126 A3.svg 7-simplex t0126 A2.svg
50 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png
t0,1,3,6{3,3,3,3,3,3}
Hexiruncitruncated 7-simplex
7-simplex t0136.svg 7-simplex t0136 A6.svg 7-simplex t0136 A5.svg 7-simplex t0136 A4.svg 7-simplex t0136 A3.svg 7-simplex t0136 A2.svg
51 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png
t0,2,3,6{3,3,3,3,3,3}
Hexiruncicantellated 7-simplex
7-simplex t0236.svg 7-simplex t0236 A6.svg 7-simplex t0236 A5.svg 7-simplex t0236 A4.svg 7-simplex t0236 A3.svg 7-simplex t0236 A2.svg
52 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png
t0,1,4,6{3,3,3,3,3,3}
Hexisteritruncated 7-simplex
7-simplex t0146.svg 7-simplex t0146 A6.svg 7-simplex t0146 A5.svg 7-simplex t0146 A4.svg 7-simplex t0146 A3.svg 7-simplex t0146 A2.svg
53 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png
t0,2,4,6{3,3,3,3,3,3}
Hexistericantellated 7-simplex
7-simplex t0246.svg 7-simplex t0246 A6.svg 7-simplex t0246 A5.svg 7-simplex t0246 A4.svg 7-simplex t0246 A3.svg 7-simplex t0246 A2.svg
54 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png
t0,1,5,6{3,3,3,3,3,3}
Hexipentitruncated 7-simplex
7-simplex t0156.svg 7-simplex t0156 A6.svg 7-simplex t0156 A5.svg 7-simplex t0156 A4.svg 7-simplex t0156 A3.svg 7-simplex t0156 A2.svg
55 CDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png
t0,1,2,3,4{3,3,3,3,3,3}
Steriruncicantitruncated 7-simplex
7-simplex t01234.svg 7-simplex t01234 A6.svg 7-simplex t01234 A5.svg 7-simplex t01234 A4.svg 7-simplex t01234 A3.svg 7-simplex t01234 A2.svg
56 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png
t0,1,2,3,5{3,3,3,3,3,3}
Pentiruncicantitruncated 7-simplex
7-simplex t01235.svg 7-simplex t01235 A6.svg 7-simplex t01235 A5.svg 7-simplex t01235 A4.svg 7-simplex t01235 A3.svg 7-simplex t01235 A2.svg
57 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png
t0,1,2,4,5{3,3,3,3,3,3}
Pentistericantitruncated 7-simplex
7-simplex t01245.svg 7-simplex t01245 A6.svg 7-simplex t01245 A5.svg 7-simplex t01245 A4.svg 7-simplex t01245 A3.svg 7-simplex t01245 A2.svg
58 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png
t0,1,3,4,5{3,3,3,3,3,3}
Pentisteriruncitruncated 7-simplex
7-simplex t01345.svg 7-simplex t01345 A6.svg 7-simplex t01345 A5.svg 7-simplex t01345 A4.svg 7-simplex t01345 A3.svg 7-simplex t01345 A2.svg
59 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png
t0,2,3,4,5{3,3,3,3,3,3}
Pentisteriruncicantellated 7-simplex
7-simplex t02345.svg 7-simplex t02345 A6.svg 7-simplex t02345 A5.svg 7-simplex t02345 A4.svg 7-simplex t02345 A3.svg 7-simplex t02345 A2.svg
60 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.png
t1,2,3,4,5{3,3,3,3,3,3}
Bisteriruncicantitruncated 7-simplex
7-simplex t12345.svg 7-simplex t12345 A6.svg 7-simplex t12345 A5.svg 7-simplex t12345 A4.svg 7-simplex t12345 A3.svg 7-simplex t12345 A2.svg
61 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png
t0,1,2,3,6{3,3,3,3,3,3}
Hexiruncicantitruncated 7-simplex
7-simplex t01236.svg 7-simplex t01236 A6.svg 7-simplex t01236 A5.svg 7-simplex t01236 A4.svg 7-simplex t01236 A3.svg 7-simplex t01236 A2.svg
62 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png
t0,1,2,4,6{3,3,3,3,3,3}
Hexistericantitruncated 7-simplex
7-simplex t01246.svg 7-simplex t01246 A6.svg 7-simplex t01246 A5.svg 7-simplex t01246 A4.svg 7-simplex t01246 A3.svg 7-simplex t01246 A2.svg
63 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png
t0,1,3,4,6{3,3,3,3,3,3}
Hexisteriruncitruncated 7-simplex
7-simplex t01346.svg 7-simplex t01346 A6.svg 7-simplex t01346 A5.svg 7-simplex t01346 A4.svg 7-simplex t01346 A3.svg 7-simplex t01346 A2.svg
64 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.png
t0,2,3,4,6{3,3,3,3,3,3}
Hexisteriruncicantellated 7-simplex
7-simplex t02346.svg 7-simplex t02346 A6.svg 7-simplex t02346 A5.svg 7-simplex t02346 A4.svg 7-simplex t02346 A3.svg 7-simplex t02346 A2.svg
65 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png
t0,1,2,5,6{3,3,3,3,3,3}
Hexipenticantitruncated 7-simplex
7-simplex t01256.svg 7-simplex t01256 A6.svg 7-simplex t01256 A5.svg 7-simplex t01256 A4.svg 7-simplex t01256 A3.svg 7-simplex t01256 A2.svg
66 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png
t0,1,3,5,6{3,3,3,3,3,3}
Hexipentiruncitruncated 7-simplex
7-simplex t01356.svg 7-simplex t01356 A6.svg 7-simplex t01356 A5.svg 7-simplex t01356 A4.svg 7-simplex t01356 A3.svg 7-simplex t01356 A2.svg
67 CDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png
t0,1,2,3,4,5{3,3,3,3,3,3}
Pentisteriruncicantitruncated 7-simplex
7-simplex t012345.svg 7-simplex t012345 A6.svg 7-simplex t012345 A5.svg 7-simplex t012345 A4.svg 7-simplex t012345 A3.svg 7-simplex t012345 A2.svg
68 CDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png
t0,1,2,3,4,6{3,3,3,3,3,3}
Hexisteriruncicantitruncated 7-simplex
7-simplex t012346.svg 7-simplex t012346 A6.svg 7-simplex t012346 A5.svg 7-simplex t012346 A4.svg 7-simplex t012346 A3.svg 7-simplex t012346 A2.svg
69 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png
t0,1,2,3,5,6{3,3,3,3,3,3}
Hexipentiruncicantitruncated 7-simplex
7-simplex t012356.svg 7-simplex t012356 A6.svg 7-simplex t012356 A5.svg 7-simplex t012356 A4.svg 7-simplex t012356 A3.svg 7-simplex t012356 A2.svg
70 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png
t0,1,2,4,5,6{3,3,3,3,3,3}
Hexipentistericantitruncated 7-simplex
7-simplex t012456.svg 7-simplex t012456 A6.svg 7-simplex t012456 A5.svg 7-simplex t012456 A4.svg 7-simplex t012456 A3.svg 7-simplex t012456 A2.svg
71 CDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.pngCDel 3a.pngCDel nodea 1.png
t0,1,2,3,4,5,6{3,3,3,3,3,3}
Omnitruncated 7-simplex
7-simplex t0123456.svg 7-simplex t0123456 A6.svg 7-simplex t0123456 A5.svg 7-simplex t0123456 A4.svg 7-simplex t0123456 A3.svg 7-simplex t0123456 A2.svg

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. "7D uniform polytopes (polyexa)".

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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All text is available under the terms of the GNU Free Documentation License