![]() 8-simplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Stericated 8-simplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Bistericated 8-simplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
![]() Steri-truncated 8-simplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Bisteri-truncated 8-simplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Steri-cantellated 8-simplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Bisteri-cantellated 8-simplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Stericanti-truncated 8-simplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Bistericanti-truncated 8-simplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Steri-runcinated 8-simplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Bisteri-runcinated 8-simplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Steriruncitruncated 8-simplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Bisterirun-citruncated 8-simplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Sterirunci-cantellated 8-simplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Bisterirunci-cantellated 8-simplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Steriruncicanti-truncated 8-simplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Bisteriruncicanti-truncated 8-simplex ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | ||
Orthogonal projections in A8 Coxeter plane |
---|
In eight-dimensional geometry, a stericated 8-simplex is a convex uniform 8-polytope with 4th order truncations ( sterication) of the regular 8-simplex. There are 16 unique sterications for the 8-simplex including permutations of truncation, cantellation, and runcination.
Stericated 8-simplex | |
---|---|
Type | uniform 8-polytope |
Schläfli symbol | t0,4{3,3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
7-faces | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 6300 |
Vertices | 630 |
Vertex figure | |
Coxeter group | A8, [37], order 362880 |
Properties | convex |
The Cartesian coordinates of the vertices of the stericated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,1,1,1,1,2). This construction is based on facets of the stericated 9-orthoplex.
Ak Coxeter plane | A8 | A7 | A6 | A5 |
---|---|---|---|---|
Graph |
![]() |
![]() |
![]() |
![]() |
Dihedral symmetry | [9] | [8] | [7] | [6] |
Ak Coxeter plane | A4 | A3 | A2 | |
Graph |
![]() |
![]() |
![]() | |
Dihedral symmetry | [5] | [4] | [3] |
bistericated 8-simplex | |
---|---|
Type | uniform 8-polytope |
Schläfli symbol | t1,5{3,3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
7-faces | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 12600 |
Vertices | 1260 |
Vertex figure | |
Coxeter group | A8, [37], order 362880 |
Properties | convex |
The Cartesian coordinates of the vertices of the bistericated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,1,1,1,1,2,2). This construction is based on facets of the bistericated 9-orthoplex.
Ak Coxeter plane | A8 | A7 | A6 | A5 |
---|---|---|---|---|
Graph |
![]() |
![]() |
![]() |
![]() |
Dihedral symmetry | [9] | [8] | [7] | [6] |
Ak Coxeter plane | A4 | A3 | A2 | |
Graph |
![]() |
![]() |
![]() | |
Dihedral symmetry | [5] | [4] | [3] |
Steritruncated 8-simplex | |
---|---|
Type | uniform 8-polytope |
Schläfli symbol | t0,1,4{3,3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
7-faces | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter group | A8, [37], order 362880 |
Properties | convex |
Ak Coxeter plane | A8 | A7 | A6 | A5 |
---|---|---|---|---|
Graph |
![]() |
![]() |
![]() |
![]() |
Dihedral symmetry | [9] | [8] | [7] | [6] |
Ak Coxeter plane | A4 | A3 | A2 | |
Graph |
![]() |
![]() |
![]() | |
Dihedral symmetry | [5] | [4] | [3] |
Bisteritruncated 8-simplex | |
---|---|
Type | uniform 8-polytope |
Schläfli symbol | t1,2,5{3,3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
7-faces | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | |
Vertices | |
Vertex figure | |
Coxeter group | A8, [37], order 362880 |
Properties | convex |
Ak Coxeter plane | A8 | A7 | A6 | A5 |
---|---|---|---|---|
Graph |
![]() |
![]() |
![]() |
![]() |
Dihedral symmetry | [9] | [8] | [7] | [6] |
Ak Coxeter plane | A4 | A3 | A2 | |
Graph |
![]() |
![]() |
![]() | |
Dihedral symmetry | [5] | [4] | [3] |
Ak Coxeter plane | A8 | A7 | A6 | A5 |
---|---|---|---|---|
Graph |
![]() |
![]() |
![]() |
![]() |
Dihedral symmetry | [9] | [8] | [7] | [6] |
Ak Coxeter plane | A4 | A3 | A2 | |
Graph |
![]() |
![]() |
![]() | |
Dihedral symmetry | [5] | [4] | [3] |
Ak Coxeter plane | A8 | A7 | A6 | A5 |
---|---|---|---|---|
Graph |
![]() |
![]() |
![]() |
![]() |
Dihedral symmetry | [9] | [8] | [7] | [6] |
Ak Coxeter plane | A4 | A3 | A2 | |
Graph |
![]() |
![]() |
![]() | |
Dihedral symmetry | [5] | [4] | [3] |
Ak Coxeter plane | A8 | A7 | A6 | A5 |
---|---|---|---|---|
Graph |
![]() |
![]() |
![]() |
![]() |
Dihedral symmetry | [9] | [8] | [7] | [6] |
Ak Coxeter plane | A4 | A3 | A2 | |
Graph |
![]() |
![]() |
![]() | |
Dihedral symmetry | [5] | [4] | [3] |
Ak Coxeter plane | A8 | A7 | A6 | A5 |
---|---|---|---|---|
Graph |
![]() |
![]() |
![]() |
![]() |
Dihedral symmetry | [9] | [8] | [7] | [6] |
Ak Coxeter plane | A4 | A3 | A2 | |
Graph |
![]() |
![]() |
![]() | |
Dihedral symmetry | [5] | [4] | [3] |
Ak Coxeter plane | A8 | A7 | A6 | A5 |
---|---|---|---|---|
Graph |
![]() |
![]() |
![]() |
![]() |
Dihedral symmetry | [9] | [8] | [7] | [6] |
Ak Coxeter plane | A4 | A3 | A2 | |
Graph |
![]() |
![]() |
![]() | |
Dihedral symmetry | [5] | [4] | [3] |
Ak Coxeter plane | A8 | A7 | A6 | A5 |
---|---|---|---|---|
Graph |
![]() |
![]() |
![]() |
![]() |
Dihedral symmetry | [9] | [8] | [7] | [6] |
Ak Coxeter plane | A4 | A3 | A2 | |
Graph |
![]() |
![]() |
![]() | |
Dihedral symmetry | [5] | [4] | [3] |
Ak Coxeter plane | A8 | A7 | A6 | A5 |
---|---|---|---|---|
Graph |
![]() |
![]() |
![]() |
![]() |
Dihedral symmetry | [9] | [8] | [7] | [6] |
Ak Coxeter plane | A4 | A3 | A2 | |
Graph |
![]() |
![]() |
![]() | |
Dihedral symmetry | [5] | [4] | [3] |
Ak Coxeter plane | A8 | A7 | A6 | A5 |
---|---|---|---|---|
Graph |
![]() |
![]() |
![]() |
![]() |
Dihedral symmetry | [9] | [8] | [7] | [6] |
Ak Coxeter plane | A4 | A3 | A2 | |
Graph |
![]() |
![]() |
![]() | |
Dihedral symmetry | [5] | [4] | [3] |
Ak Coxeter plane | A8 | A7 | A6 | A5 |
---|---|---|---|---|
Graph |
![]() |
![]() |
![]() |
![]() |
Dihedral symmetry | [9] | [8] | [7] | [6] |
Ak Coxeter plane | A4 | A3 | A2 | |
Graph |
![]() |
![]() |
![]() | |
Dihedral symmetry | [5] | [4] | [3] |
Ak Coxeter plane | A8 | A7 | A6 | A5 |
---|---|---|---|---|
Graph |
![]() |
![]() |
![]() |
![]() |
Dihedral symmetry | [9] | [8] | [7] | [6] |
Ak Coxeter plane | A4 | A3 | A2 | |
Graph |
![]() |
![]() |
![]() | |
Dihedral symmetry | [5] | [4] | [3] |
Ak Coxeter plane | A8 | A7 | A6 | A5 |
---|---|---|---|---|
Graph |
![]() |
![]() |
![]() |
![]() |
Dihedral symmetry | [9] | [8] | [7] | [6] |
Ak Coxeter plane | A4 | A3 | A2 | |
Graph |
![]() |
![]() |
![]() | |
Dihedral symmetry | [5] | [4] | [3] |
Ak Coxeter plane | A8 | A7 | A6 | A5 |
---|---|---|---|---|
Graph |
![]() |
![]() |
![]() |
![]() |
Dihedral symmetry | [9] | [8] | [7] | [6] |
Ak Coxeter plane | A4 | A3 | A2 | |
Graph |
![]() |
![]() |
![]() | |
Dihedral symmetry | [5] | [4] | [3] |
This polytope is one of 135 uniform 8-polytopes with A8 symmetry.