Orthogonal projections in B5 Coxeter plane |
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In five-dimensional geometry, a steric 5-cube or (steric 5-demicube or sterihalf 5-cube) is a convex uniform 5-polytope. There are unique 4 steric forms of the 5-cube. Steric 5-cubes have half the vertices of stericated 5-cubes.
Steric 5-cube | |
---|---|
Type | uniform polyteron |
Schläfli symbol |
|
Coxeter-Dynkin diagram | |
4-faces | 82 |
Cells | 480 |
Faces | 720 |
Edges | 400 |
Vertices | 80 |
Vertex figure | {3,3}-t1{3,3} antiprism |
Coxeter groups | D5, [32,1,1] |
Properties | convex |
The Cartesian coordinates for the 80 vertices of a steric 5-cube centered at the origin are the permutations of
with an odd number of plus signs.
Coxeter plane | B5 | |
---|---|---|
Graph | ||
Dihedral symmetry | [10/2] | |
Coxeter plane | D5 | D4 |
Graph | ||
Dihedral symmetry | [8] | [6] |
Coxeter plane | D3 | A3 |
Graph | ||
Dihedral symmetry | [4] | [4] |
Dimensional family of steric n-cubes | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
n | 5 | 6 | 7 | 8 | |||||||
[1+,4,3n-2] = [3,3n-3,1] |
[1+,4,33] = [3,32,1] |
[1+,4,34] = [3,33,1] |
[1+,4,35] = [3,34,1] |
[1+,4,36] = [3,35,1] | |||||||
Steric figure |
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Coxeter | = |
= |
= |
= | |||||||
Schläfli | h4{4,33} | h4{4,34} | h4{4,35} | h4{4,36} |
Stericantic 5-cube | |
---|---|
Type | uniform polyteron |
Schläfli symbol |
|
Coxeter-Dynkin diagram | |
4-faces | 82 |
Cells | 720 |
Faces | 1840 |
Edges | 1680 |
Vertices | 480 |
Vertex figure | |
Coxeter groups | D5, [32,1,1] |
Properties | convex |
The Cartesian coordinates for the 480 vertices of a stericantic 5-cube centered at the origin are coordinate permutations:
with an odd number of plus signs.
Coxeter plane | B5 | |
---|---|---|
Graph | ||
Dihedral symmetry | [10/2] | |
Coxeter plane | D5 | D4 |
Graph | ||
Dihedral symmetry | [8] | [6] |
Coxeter plane | D3 | A3 |
Graph | ||
Dihedral symmetry | [4] | [4] |
Steriruncic 5-cube | |
---|---|
Type | uniform polyteron |
Schläfli symbol |
|
Coxeter-Dynkin diagram | |
4-faces | 82 |
Cells | 560 |
Faces | 1280 |
Edges | 1120 |
Vertices | 320 |
Vertex figure | |
Coxeter groups | D5, [32,1,1] |
Properties | convex |
The Cartesian coordinates for the 320 vertices of a steriruncic 5-cube centered at the origin are coordinate permutations:
with an odd number of plus signs.
Coxeter plane | B5 | |
---|---|---|
Graph | ||
Dihedral symmetry | [10/2] | |
Coxeter plane | D5 | D4 |
Graph | ||
Dihedral symmetry | [8] | [6] |
Coxeter plane | D3 | A3 |
Graph | ||
Dihedral symmetry | [4] | [4] |
Steriruncicantic 5-cube | |
---|---|
Type | uniform polyteron |
Schläfli symbol |
|
Coxeter-Dynkin diagram | |
4-faces | 82 |
Cells | 720 |
Faces | 2080 |
Edges | 2400 |
Vertices | 960 |
Vertex figure | |
Coxeter groups | D5, [32,1,1] |
Properties | convex |
The Cartesian coordinates for the 960 vertices of a steriruncicantic 5-cube centered at the origin are coordinate permutations:
with an odd number of plus signs.
Coxeter plane | B5 | |
---|---|---|
Graph | ||
Dihedral symmetry | [10/2] | |
Coxeter plane | D5 | D4 |
Graph | ||
Dihedral symmetry | [8] | [6] |
Coxeter plane | D3 | A3 |
Graph | ||
Dihedral symmetry | [4] | [4] |
This polytope is based on the 5-demicube, a part of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family.
There are 23 uniform polytera (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.
D5 polytopes | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
h{4,3,3,3} |
h2{4,3,3,3} |
h3{4,3,3,3} |
h4{4,3,3,3} |
h2,3{4,3,3,3} |
h2,4{4,3,3,3} |
h3,4{4,3,3,3} |
h2,3,4{4,3,3,3} |