Pentellated 6-orthoplex
Encyclopedia
| Orthogonal projections in BC6 Coxeter plane | |||
|---|---|---|---|
6-orthoplex |
Pentellated 6-orthoplex Pentellated 6-cube Pentellated 6-cube In six-dimensional geometry, a pentellated 6-cube is a convex uniform 6-polytope with 5th order truncations of the regular 6-cube.There are unique 16 degrees of pentellations of the 6-cube with permutations of truncations, cantellations, runcinations, and sterications... |
6-cube |
Pentitruncated 6-orthoplex |
Penticantellated 6-orthoplex |
Penticantitruncated 6-orthoplex |
Pentiruncitruncated 6-orthoplex |
Pentiruncicantellated 6-cube |
Pentiruncicantitruncated 6-orthoplex |
Pentisteritruncated 6-cube |
Pentistericantitruncated 6-orthoplex |
Pentisteriruncicantitruncated 6-orthoplex (Omnitruncated 6-cube) |
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 pentellated 6-orthoplex is a convex uniform 6-polytope with 5th 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 :...
of the regular 6-orthoplex.
There are unique 16 degrees of pentellations of the 6-orthoplex with permutations of truncations, cantellations, runcinations, and sterications. Ten are shown, with the other 6 more easily constructed as a pentellated 6-cube
Pentellated 6-cube
In six-dimensional geometry, a pentellated 6-cube is a convex uniform 6-polytope with 5th order truncations of the regular 6-cube.There are unique 16 degrees of pentellations of the 6-cube with permutations of truncations, cantellations, runcinations, and sterications...
. The simple pentellated 6-orthoplex (Same as pentellated 5-cube) is also called an expanded 6-orthoplex, constructed by an expansion
Expansion (geometry)
In geometry, expansion is a polytope operation where facets are separated and moved radially apart, and new facets are formed at separated elements...
operation applied to the regular 6-orthoplex. The highest form, the pentisteriruncicantitruncated 6-orthoplex, is called an omnitruncated 6-orthoplex with all of the nodes ringed.
Pentitruncated 6-orthoplex
| Pentitruncated 6-orthoplex | |
|---|---|
| Type | uniform polypeton |
| Schläfli symbol | t0,1,5{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 |
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| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | 8640 |
| Vertices | 1920 |
| 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... |
Penticantellated 6-orthoplex
| Penticantellated 6-orthoplex | |
|---|---|
| Type | uniform polypeton |
| Schläfli symbol | t0,2,5{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 | 21120 |
| 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... |
Penticantitruncated 6-orthoplex
| Penticantitruncated 6-orthoplex | |
|---|---|
| Type | uniform polypeton |
| Schläfli symbol | t0,1,2,5{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 | 30720 |
| Vertices | 7680 |
| 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
- Terigreatorhombated hexacontitetrapeton (Acronym: togrig) (Jonathan Bowers)
Pentiruncitruncated 6-orthoplex
| Pentiruncitruncated 6-orthoplex | |
|---|---|
| Type | uniform polypeton |
| Schläfli symbol | t0,1,3,5{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 | 51840 |
| 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
- Teriprismatotruncated hexacontitetrapeton (Acronym: tocrax) (Jonathan Bowers)
Pentiruncicantitruncated 6-orthoplex
| Pentiruncicantitruncated 6-orthoplex | |
|---|---|
| Type | uniform polypeton |
| Schläfli symbol | t0,1,2,3,5{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 | 80640 |
| 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... |
Alternate names
- Terigreatoprismated hexacontitetrapeton (Acronym: tagpog) (Jonathan Bowers)
Pentistericantitruncated 6-orthoplex
| Pentistericantitruncated 6-orthoplex | |
|---|---|
| Type | uniform polypeton |
| Schläfli symbol | t0,1,2,4,5{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 | 80640 |
| 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... |
Alternate names
- Tericelligreatorhombated hexacontitetrapeton (Acronym: tecagorg) (Jonathan Bowers)