Hexicated 8-simplex | |
---|---|
![]() Orthogonal projection on A8 Coxeter plane | |
Type | uniform 8-polytope |
Schläfli symbol | t0,6{3,3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
7-faces | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 2268 |
Vertices | 252 |
Vertex figure | |
Coxeter groups | A8, [37], order 362880 |
Properties | convex |
In eight-dimensional geometry, a hexicated 8-simplex is a uniform 8-polytope, being a hexication (6th order truncation) of the regular 8-simplex.
The Cartesian coordinates of the vertices of the hexicated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,1,1,1,1,1,2). This construction is based on facets of the hexicated 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] |
This polytope is one of 135 uniform 8-polytopes with A8 symmetry.
Hexicated 8-simplex | |
---|---|
![]() Orthogonal projection on A8 Coxeter plane | |
Type | uniform 8-polytope |
Schläfli symbol | t0,6{3,3,3,3,3,3,3} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
7-faces | |
6-faces | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 2268 |
Vertices | 252 |
Vertex figure | |
Coxeter groups | A8, [37], order 362880 |
Properties | convex |
In eight-dimensional geometry, a hexicated 8-simplex is a uniform 8-polytope, being a hexication (6th order truncation) of the regular 8-simplex.
The Cartesian coordinates of the vertices of the hexicated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,1,1,1,1,1,2). This construction is based on facets of the hexicated 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] |
This polytope is one of 135 uniform 8-polytopes with A8 symmetry.