Stericated 6-demicube
Encyclopedia
6-cube |
stericated 6-demicube |
Steritruncated 6-demicube |
Stericantellated 6-demicube |
Stericantitruncated 6-demicube |
steriruncinated 6-demicube |
Steriruncitruncated 6-demicube |
Steriruncicantellated 6-demicube |
Steriruncicantitruncated 6-demicube |
| Orthogonal projections in D6 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-demicube is a convex uniform 6-polytope, constructed as a sterication (4th order truncation) of the 6-demicube.
There are 8 unique sterications of the 6-demicube, including permutations of truncations, cantellations, and runcinations.
Stericated 6-demicube
| Stericated 6-demicube | |
|---|---|
| Type | uniform polypeton |
| Schläfli symbol | t0,4{3,34,1} |
| 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... |
|
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | 1440 |
| Vertices | 192 |
| 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 |
D6, [33,1,1] |
| 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
- stericated demihexeract
- Small cellated hemihexeract (Acronym: sochax) (Jonathan Bowers)
Cartesian coordinates
The Cartesian coordinates for the vertices of a stericated demihexeract centered at the origin are coordinate permutations:- (±1,±1,±1,±1,±1,±3)
with an odd number of plus signs.
Steritruncated 6-demicube
| Steritruncated 6-demicube | |
|---|---|
| Type | uniform polypeton |
| Schläfli symbol | t0,1,4{3,34,1} |
| 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... |
|
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | 9600 |
| 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 |
D6, [33,1,1] |
| 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... |
Cartesian coordinates
The Cartesian coordinates for the vertices of a stericantitruncated demihexeract centered at the origin are coordinate permutations:- (±1,±1,±3,±3,±3,±5)
with an odd number of plus signs.
Stericantellated 6-demicube
| Stericantellated 6-demicube | |
|---|---|
| Type | uniform polypeton |
| Schläfli symbol | t0,2,4{3,34,1} |
| 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... |
|
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | 10560 |
| 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 |
D6, [33,1,1] |
| 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... |
Cartesian coordinates
The Cartesian coordinates for the vertices of a stericantellated demihexeract centered at the origin are coordinate permutations:- (±1,±1,±1,±3,±3,±5)
with an odd number of plus signs.
Stericantitruncated 6-demicube
| Stericantitruncated 6-demicube | |
|---|---|
| Type | uniform polypeton |
| Schläfli symbol | t0,1,2,4{3,32,1} |
| Coxeter symbol | t0,1,2,4(131) |
| 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... |
|
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | 20160 |
| 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 |
D6, [33,1,1] |
| 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... |
Cartesian coordinates
The Cartesian coordinates for the vertices of a stericantitruncated demihexeract centered at the origin are coordinate permutations:- (±1,±1,±3,±3,±5,±7)
with an odd number of plus signs.
Steriruncinated 6-demicube
| Steriruncinated 6-demicube | |
|---|---|
| Type | uniform polypeton |
| Schläfli symbol | t0,3,4{3,34,1} |
| 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... |
|
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | 5280 |
| 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 |
D6, [33,1,1] |
| 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
- Steriruncinated demihexeract
- Small cellipriamated hemihexeract (Acronym: cophix) (Jonathan Bowers)
Cartesian coordinates
The Cartesian coordinates for the vertices of a Steriruncicated demihexeract centered at the origin are coordinate permutations:- (±1,±1,±1,±1,±3,±5)
with an odd number of plus signs.
Steriruncitruncated 6-demicube
| Steriruncitruncated 6-demicube | |
|---|---|
| Type | uniform polypeton |
| Schläfli symbol | t0,1,3,4{3,34,1} |
| 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... |
|
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | 23040 |
| 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 |
D6, [33,1,1] |
| 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... |
Cartesian coordinates
The Cartesian coordinates for the vertices of a Steriruncicantitruncated demihexeract centered at the origin are coordinate permutations:- (±1,±1,±3,±3,±5,±7)
with an odd number of plus signs.
Steriruncicantellated 6-demicube
| Steriruncicantellated 6-demicube | |
|---|---|
| Type | uniform polypeton |
| Schläfli symbol | t0,2,3,4{3,34,1} |
| 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... |
|
| 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 |
D6, [33,1,1] |
| 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... |
Cartesian coordinates
The Cartesian coordinates for the vertices of a Steriruncicantellated demihexeract centered at the origin are coordinate permutations:- (±1,±1,±1,±3,±5,±7)
with an odd number of plus signs.
Steriruncicantitruncated 6-demicube
| Steriruncicantitruncated 6-demicube | |
|---|---|
| Type | uniform polypeton |
| Schläfli symbol | t0,1,2,3,4{3,32,1} |
| Coxeter symbol | t0,1,2,3,4(131) |
| 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... |
|
| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | 34560 |
| 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 |
D6, [33,1,1] |
| 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... |
Cartesian coordinates
The Cartesian coordinates for the vertices of a Steriruncicantitruncated demihexeract centered at the origin are coordinate permutations:- (±1,±1,±3,±3,±5,±7)
with an odd number of plus signs.