Cantellated 5-demicube
Encyclopedia
5-cube |
Cantellated 5-demicube |
Cantitruncated 5-demicube |
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| Orthogonal projections in D5 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 cantellated 5-demicube is a convex uniform 5-polytope, being a cantellation of the uniform 5-demicube.
There are 2 unique cantellation for the 5-demicube including a truncation.
Cantellated 5-demicube
| Cantellated 5-demicube | |
|---|---|
| Type | uniform polyteron Uniform polyteron In geometry, a uniform polyteron is a five-dimensional uniform polytope. By definition, a uniform polyteron is vertex-transitive and constructed from uniform polychoron facets.... |
| Schläfli symbol | t0,2{3,32,1} |
| 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... |
|
| 4-faces | 42 |
| Cells | 360 |
| Faces | 880 |
| Edges | 720 |
| Vertices | 160 |
| 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 |
D5, [32,1,1] |
| 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 960 vertices of a cantellated demipenteract centered at the origin are coordinate permutations:- (±1,±1,±1,±3,±3)
with an odd number of plus signs.
Cantitruncated 5-demicube
| Cantitruncated 5-demicube | |
|---|---|
| Type | uniform polyteron Uniform polyteron In geometry, a uniform polyteron is a five-dimensional uniform polytope. By definition, a uniform polyteron is vertex-transitive and constructed from uniform polychoron facets.... |
| Schläfli symbol | t0,1,2{3,32,1} |
| 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... |
|
| 4-faces | 42 |
| Cells | 360 |
| Faces | 1040 |
| Edges | 1200 |
| Vertices | 480 |
| 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 |
D5, [32,1,1] |
| 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 480 vertices of a cantitruncated demipenteract centered at the origin are coordinate permutations:- (±1,±1,±3,±5,±5)
with an odd number of plus signs.
Related polytopes
This polytope is based on the 5-demicube, a part of a dimensional family of uniform polytopeUniform polytope
A uniform polytope is a vertex-transitive polytope made from uniform polytope facets of a lower dimension. Uniform polytopes of 2 dimensions are the regular polygons....
s called demihypercubes for being alternation of the hypercube
Hypercube
In geometry, a hypercube is an n-dimensional analogue of a square and a cube . It is a closed, compact, convex figure whose 1-skeleton consists of groups of opposite parallel line segments aligned in each of the space's dimensions, perpendicular to each other and of the same length.An...
family.
There are 23 uniform polytera
Uniform polyteron
In geometry, a uniform polyteron is a five-dimensional uniform polytope. By definition, a uniform polyteron is vertex-transitive and constructed from uniform polychoron facets....
(uniform 5-polytope) that can be constructed from the D5 symmetry of the 5-demicube, of which are unique to this family, and 15 are shared within the 5-cube family.