Stericated 8-simplex
Encyclopedia
8-simplex |
Stericated 8-simplex |
Bistericated 8-simplex |
|
Steritruncated 8-simplex |
Bisteritruncated 8-simplex |
Stericantellated 8-simplex |
Bistericantellated 8-simplex |
Stericantitruncated 8-simplex |
Bistericantitruncated 8-simplex |
Steriruncinated 8-simplex |
Bisteriruncinated 8-simplex |
Steriruncitruncated 8-simplex |
Bisteriruncitruncated 8-simplex |
Steriruncicantellated 8-simplex |
Bisteriruncicantellated 8-simplex |
Steriruncicantitruncated 8-simplex |
Bisteriruncicantitruncated 8-simplex |
||
| Orthogonal projections in A8 Coxeter plane | |||
|---|---|---|---|
In eight-dimensional geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, a stericated 8-simplex is a convex uniform 8-polytope with 4th order truncations
Truncation (geometry)
In geometry, a truncation is an operation in any dimension that cuts polytope vertices, creating a new facet in place of each vertex.- Uniform truncation :...
(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
| Stericated 8-simplex | |
|---|---|
| Type | uniform polyzetton |
| Schläfli symbol | t0,4{3,3,3,3,3,3,3} |
| Coxeter-Dynkin diagram Coxeter-Dynkin diagram In geometry, a Coxeter–Dynkin diagram is a graph with numerically labeled edges representing the spatial relations between a collection of mirrors... s |
|
| 7-faces | |
| 6-faces | |
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | 6300 |
| Vertices | 630 |
| Vertex figure Vertex figure In geometry a vertex figure is, broadly speaking, the figure exposed when a corner of a polyhedron or polytope is sliced off.-Definitions - theme and variations:... |
|
| Coxeter group Coxeter group In mathematics, a Coxeter group, named after H.S.M. Coxeter, is an abstract group that admits a formal description in terms of mirror symmetries. Indeed, the finite Coxeter groups are precisely the finite Euclidean reflection groups; the symmetry groups of regular polyhedra are an example... |
A8, [37], order 362880 |
| Properties | convex Convex polytope A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn... |
Coordinates
The Cartesian coordinates of the vertices of the stericated 8-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,1,1,1,1,2). This construction is based on facets of the stericated 9-orthoplex.Bistericated 8-simplex
| bistericated 8-simplex | |
|---|---|
| Type | uniform polyzetton |
| Schläfli symbol | t1,5{3,3,3,3,3,3,3} |
| Coxeter-Dynkin diagram Coxeter-Dynkin diagram In geometry, a Coxeter–Dynkin diagram is a graph with numerically labeled edges representing the spatial relations between a collection of mirrors... s |
|
| 7-faces | |
| 6-faces | |
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | 12600 |
| Vertices | 1260 |
| Vertex figure Vertex figure In geometry a vertex figure is, broadly speaking, the figure exposed when a corner of a polyhedron or polytope is sliced off.-Definitions - theme and variations:... |
|
| Coxeter group Coxeter group In mathematics, a Coxeter group, named after H.S.M. Coxeter, is an abstract group that admits a formal description in terms of mirror symmetries. Indeed, the finite Coxeter groups are precisely the finite Euclidean reflection groups; the symmetry groups of regular polyhedra are an example... |
A8, [37], order 362880 |
| Properties | convex Convex polytope A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn... |
Coordinates
The Cartesian coordinates of the vertices of the bistericated 8-simplex can be most simply positioned in 8-space as permutations of (0,0,0,0,1,1,1,1,2). This construction is based on facets of the bistericated 9-orthoplex.Steritruncated 8-simplex
| Steritruncated 8-simplex | |
|---|---|
| Type | uniform polyzetton |
| Schläfli symbol | t0,1,4{3,3,3,3,3,3,3} |
| Coxeter-Dynkin diagram Coxeter-Dynkin diagram In geometry, a Coxeter–Dynkin diagram is a graph with numerically labeled edges representing the spatial relations between a collection of mirrors... s |
|
| 7-faces | |
| 6-faces | |
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | |
| Vertices | |
| Vertex figure Vertex figure In geometry a vertex figure is, broadly speaking, the figure exposed when a corner of a polyhedron or polytope is sliced off.-Definitions - theme and variations:... |
|
| Coxeter group Coxeter group In mathematics, a Coxeter group, named after H.S.M. Coxeter, is an abstract group that admits a formal description in terms of mirror symmetries. Indeed, the finite Coxeter groups are precisely the finite Euclidean reflection groups; the symmetry groups of regular polyhedra are an example... |
A8, [37], order 362880 |
| Properties | convex Convex polytope A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn... |
Bisteritruncated 8-simplex
| Bisteritruncated 8-simplex | |
|---|---|
| Type | uniform polyzetton |
| Schläfli symbol | t1,2,5{3,3,3,3,3,3,3} |
| Coxeter-Dynkin diagram Coxeter-Dynkin diagram In geometry, a Coxeter–Dynkin diagram is a graph with numerically labeled edges representing the spatial relations between a collection of mirrors... s |
|
| 7-faces | |
| 6-faces | |
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | |
| Vertices | |
| Vertex figure Vertex figure In geometry a vertex figure is, broadly speaking, the figure exposed when a corner of a polyhedron or polytope is sliced off.-Definitions - theme and variations:... |
|
| Coxeter group Coxeter group In mathematics, a Coxeter group, named after H.S.M. Coxeter, is an abstract group that admits a formal description in terms of mirror symmetries. Indeed, the finite Coxeter groups are precisely the finite Euclidean reflection groups; the symmetry groups of regular polyhedra are an example... |
A8, [37], order 362880 |
| Properties | convex Convex polytope A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn... |