A6 polytope

6-simplex

In 6-dimensional geometry, there are 35 uniform polytopes with A₆ symmetry. There is one self-dual regular form, the 6-simplex with 7 vertices.
Each can be visualized as symmetric orthographic projections in Coxeter planes of the A₆ Coxeter group, and other subgroups.

Graphs

Symmetric orthographic projections of these 35 polytopes can be made in the A₆, A₅, A₄, A₃, A₂ Coxeter planes. A_k graphs have ' symmetry. For even k and symmetric ringed diagrams, symmetry doubles to '.
These 35 polytopes are each shown in these 5 symmetry planes, with vertices and edges drawn, and vertices colored by the number of overlapping vertices in each projective position.

#	A₆	A₅	A₄	A₃	A₂	Coxeter-Dynkin diagram Schläfli symbol Name
1						t₀ 6-simplex Heptapeton
2						t₁ Rectified 6-simplex Rectified heptapeton
3						t_0,1 Truncated 6-simplex Truncated heptapeton
4						t₂ Birectified 6-simplex Birectified heptapeton
5						t_0,2 Cantellated 6-simplex Small rhombated heptapeton
6						t_1,2 Bitruncated 6-simplex Bitruncated heptapeton
7						t_0,1,2 Cantitruncated 6-simplex Great rhombated heptapeton
8						t_0,3 Runcinated 6-simplex Small prismated heptapeton
9						t_1,3 Bicantellated 6-simplex Small birhombated heptapeton
10						t_0,1,3 Runcitruncated 6-simplex Prismatotruncated heptapeton
11						t_2,3 Tritruncated 6-simplex Tetradecapeton
12						t_0,2,3 Runcicantellated 6-simplex Prismatorhombated heptapeton
13						t_1,2,3 Bicantitruncated 6-simplex Great birhombated heptapeton
14						t_0,1,2,3 Runcicantitruncated 6-simplex Great prismated heptapeton
15						t_0,4 Stericated 6-simplex Small cellated heptapeton
16						t_1,4 Biruncinated 6-simplex Small biprismato-tetradecapeton
17						t_0,1,4 Steritruncated 6-simplex cellitruncated heptapeton
18						t_0,2,4 Stericantellated 6-simplex Cellirhombated heptapeton
19						t_1,2,4 Biruncitruncated 6-simplex Biprismatorhombated heptapeton
20						t_0,1,2,4 Stericantitruncated 6-simplex Celligreatorhombated heptapeton
21						t_0,3,4 Steriruncinated 6-simplex Celliprismated heptapeton
22						t_0,1,3,4 Steriruncitruncated 6-simplex celliprismatotruncated heptapeton
23						t_0,2,3,4 Steriruncicantellated 6-simplex celliprismatorhombated heptapeton
24						t_1,2,3,4 Biruncicantitruncated 6-simplex Great biprismato-tetradecapeton
25						t_0,1,2,3,4 Steriruncicantitruncated 6-simplex Great cellated heptapeton
26						t_0,5 Pentellated 6-simplex Small teri-tetradecapeton
27						t_0,1,5 Pentitruncated 6-simplex Tericellated heptapeton
28						t_0,2,5 Penticantellated 6-simplex Teriprismated heptapeton
29						t_0,1,2,5 Penticantitruncated 6-simplex Terigreatorhombated heptapeton
30						t_0,1,3,5 Pentiruncitruncated 6-simplex Tericellirhombated heptapeton
31						t_0,2,3,5 Pentiruncicantellated 6-simplex Teriprismatorhombi-tetradecapeton
32						t_0,1,2,3,5 Pentiruncicantitruncated 6-simplex Terigreatoprismated heptapeton
33						t_0,1,4,5 Pentisteritruncated 6-simplex tericellitrunki-tetradecapeton
34						t_0,1,2,4,5 Pentistericantitruncated 6-simplex tericelligreatorhombated heptapeton
35						t_0,1,2,3,4,5 Omnitruncated 6-simplex Great teri-tetradecapeton