Stericated 6-orthoplex
Encyclopedia
6-orthoplex |
Stericated 6-orthoplex |
Steritruncated 6-orthoplex |
Stericantellated 6-orthoplex |
Stericantitruncated 6-orthoplex |
Steriruncinated 6-orthoplex |
Steriruncitruncated 6-orthoplex |
Steriruncicantellated 6-orthoplex |
Steriruncicantitruncated 6-orthoplex |
| Orthogonal projections in BC6 Coxeter plane | ||
|---|---|---|
In six-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 6-orthoplex is a convex uniform 6-polytope, constructed as a sterication (4th order truncation) of the regular 6-orthoplex.
There are 16 unique sterications for the 6-orthoplex with permutations of truncations, cantellations, and runcinations. Eight are better represented from the stericated 6-cube
Stericated 6-cube
In six-dimensional geometry, a stericated 6-cube is a convex uniform 6-polytope, constructed as a sterication of the regular 6-cube....
.
Stericated 6-orthoplex
| Stericated 6-orthoplex | |
|---|---|
| Type | uniform polypeton |
| Schläfli symbol | t0,4{3,3,3,3,4} |
| 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 |
|
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | 5760 |
| Vertices | 960 |
| 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... s |
BC6, [4,3,3,3,3] |
| 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... |
Steritruncated 6-orthoplex
| Steritruncated 6-orthoplex | |
|---|---|
| Type | uniform polypeton |
| Schläfli symbol | t0,1,4{3,3,3,3,4} |
| 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 |
|
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | 19200 |
| Vertices | 3840 |
| 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... s |
BC6, [4,3,3,3,3] |
| 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... |
Stericantellated 6-orthoplex
| Stericantellated 6-orthoplex | |
|---|---|
| Type | uniform polypeton |
| Schläfli symbol | t0,2,4{3,3,3,3,4} |
| 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 |
|
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | 28800 |
| Vertices | 5760 |
| 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... s |
BC6, [4,3,3,3,3] |
| 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... |
Stericantitruncated 6-orthoplex
| stericantitruncated 6-orthoplex | |
|---|---|
| Type | uniform polypeton |
| Schläfli symbol | t0,1,2,4{3,3,3,3,4} |
| 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 |
|
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | 46080 |
| Vertices | 11520 |
| 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... s |
BC6, [4,3,3,3,3] |
| 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... |
Alternate names
- Celligreatorhombated hexacontatetrapeton (Acronym: cagorg) (Jonathan Bowers)
Steriruncinated 6-orthoplex
| steriruncinated 6-orthoplex | |
|---|---|
| Type | uniform polypeton |
| Schläfli symbol | t0,3,4{3,3,3,3,4} |
| 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 |
|
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | 15360 |
| Vertices | 3840 |
| 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... s |
BC6, [4,3,3,3,3] |
| 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... |
Steriruncitruncated 6-orthoplex
| steriruncitruncated 6-orthoplex | |
|---|---|
| Type | uniform polypeton |
| Schläfli symbol | t0,1,3,4{3,3,3,3,4} |
| 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 |
|
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | 40320 |
| Vertices | 11520 |
| 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... s |
BC6, [4,3,3,3,3] |
| 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... |
Alternate names
- Celliprismatotruncated hexacontatetrapeton (Acronym: captog) (Jonathan Bowers)
Steriruncicantellated 6-orthoplex
| steriruncicantellated 6-orthoplex | |
|---|---|
| Type | uniform polypeton |
| Schläfli symbol | t0,2,3,4{3,3,3,3,4} |
| 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 |
|
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | 40320 |
| Vertices | 11520 |
| 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... s |
BC6, [4,3,3,3,3] |
| 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... |
Alternate names
- Celliprismatorhombated hexacontatetrapeton (Acronym: coprag) (Jonathan Bowers)
Steriruncicantitruncated 6-orthoplex
| Steriuncicantitruncated 6-orthoplex | |
|---|---|
| Type | uniform polypeton |
| Schläfli symbol | t0,1,2,3,4{3,3,3,3,4} |
| 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 |
|
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | 69120 |
| Vertices | 23040 |
| 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... s |
BC6, [4,3,3,3,3] |
| 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... |