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 |
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In six-dimensional geometry, 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 | |
---|---|
Type | uniform polypeton |
Schläfli symbol | t0,4{3,34,1} |
Coxeter-Dynkin diagram | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 1440 |
Vertices | 192 |
Vertex figure | |
Coxeter groups | D6, [33,1,1] |
Properties | convex |
The Cartesian coordinates for the vertices of a stericated demihexeract centered at the origin are coordinate permutations:
with an odd number of plus signs.
Coxeter plane | B6 | |
---|---|---|
Graph | ||
Dihedral symmetry | [12/2] | |
Coxeter plane | D6 | D5 |
Graph | ||
Dihedral symmetry | [10] | [8] |
Coxeter plane | D4 | D3 |
Graph | ||
Dihedral symmetry | [6] | [4] |
Coxeter plane | A5 | A3 |
Graph | ||
Dihedral symmetry | [6] | [4] |
Steritruncated 6-demicube | |
---|---|
Type | uniform polypeton |
Schläfli symbol | t0,1,4{3,34,1} |
Coxeter-Dynkin diagram | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 9600 |
Vertices | 1920 |
Vertex figure | |
Coxeter groups | D6, [33,1,1] |
Properties | convex |
The Cartesian coordinates for the vertices of a stericantitruncated demihexeract centered at the origin are coordinate permutations:
with an odd number of plus signs.
Coxeter plane | B6 | |
---|---|---|
Graph | ||
Dihedral symmetry | [12/2] | |
Coxeter plane | D6 | D5 |
Graph | ||
Dihedral symmetry | [10] | [8] |
Coxeter plane | D4 | D3 |
Graph | ||
Dihedral symmetry | [6] | [4] |
Coxeter plane | A5 | A3 |
Graph | ||
Dihedral symmetry | [6] | [4] |
Stericantellated 6-demicube | |
---|---|
Type | uniform polypeton |
Schläfli symbol | t0,2,4{3,34,1} |
Coxeter-Dynkin diagram | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 10560 |
Vertices | 1920 |
Vertex figure | |
Coxeter groups | D6, [33,1,1] |
Properties | convex |
The Cartesian coordinates for the vertices of a stericantellated demihexeract centered at the origin are coordinate permutations:
with an odd number of plus signs.
Coxeter plane | B6 | |
---|---|---|
Graph | ||
Dihedral symmetry | [12/2] | |
Coxeter plane | D6 | D5 |
Graph | ||
Dihedral symmetry | [10] | [8] |
Coxeter plane | D4 | D3 |
Graph | ||
Dihedral symmetry | [6] | [4] |
Coxeter plane | A5 | A3 |
Graph | ||
Dihedral symmetry | [6] | [4] |
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 | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 20160 |
Vertices | 5760 |
Vertex figure | |
Coxeter groups | D6, [33,1,1] |
Properties | convex |
The Cartesian coordinates for the vertices of a stericantitruncated demihexeract centered at the origin are coordinate permutations:
with an odd number of plus signs.
Coxeter plane | B6 | |
---|---|---|
Graph | ||
Dihedral symmetry | [12/2] | |
Coxeter plane | D6 | D5 |
Graph | ||
Dihedral symmetry | [10] | [8] |
Coxeter plane | D4 | D3 |
Graph | ||
Dihedral symmetry | [6] | [4] |
Coxeter plane | A5 | A3 |
Graph | ||
Dihedral symmetry | [6] | [4] |
Steriruncinated 6-demicube | |
---|---|
Type | uniform polypeton |
Schläfli symbol | t0,3,4{3,34,1} |
Coxeter-Dynkin diagram | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 5280 |
Vertices | 960 |
Vertex figure | |
Coxeter groups | D6, [33,1,1] |
Properties | convex |
The Cartesian coordinates for the vertices of a Steriruncicated demihexeract centered at the origin are coordinate permutations:
with an odd number of plus signs.
Coxeter plane | B6 | |
---|---|---|
Graph | ||
Dihedral symmetry | [12/2] | |
Coxeter plane | D6 | D5 |
Graph | ||
Dihedral symmetry | [10] | [8] |
Coxeter plane | D4 | D3 |
Graph | ||
Dihedral symmetry | [6] | [4] |
Coxeter plane | A5 | A3 |
Graph | ||
Dihedral symmetry | [6] | [4] |
Steriruncitruncated 6-demicube | |
---|---|
Type | uniform polypeton |
Schläfli symbol | t0,1,3,4{3,34,1} |
Coxeter-Dynkin diagram | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 23040 |
Vertices | 5760 |
Vertex figure | |
Coxeter groups | D6, [33,1,1] |
Properties | convex |
The Cartesian coordinates for the vertices of a Steriruncicantitruncated demihexeract centered at the origin are coordinate permutations:
with an odd number of plus signs.
Coxeter plane | B6 | |
---|---|---|
Graph | ||
Dihedral symmetry | [12/2] | |
Coxeter plane | D6 | D5 |
Graph | ||
Dihedral symmetry | [10] | [8] |
Coxeter plane | D4 | D3 |
Graph | ||
Dihedral symmetry | [6] | [4] |
Coxeter plane | A5 | A3 |
Graph | ||
Dihedral symmetry | [6] | [4] |
Steriruncicantellated 6-demicube | |
---|---|
Type | uniform polypeton |
Schläfli symbol | t0,2,3,4{3,34,1} |
Coxeter-Dynkin diagram | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 15360 |
Vertices | 3840 |
Vertex figure | |
Coxeter groups | D6, [33,1,1] |
Properties | convex |
The Cartesian coordinates for the vertices of a Steriruncicantellated demihexeract centered at the origin are coordinate permutations:
with an odd number of plus signs.
Coxeter plane | B6 | |
---|---|---|
Graph | ||
Dihedral symmetry | [12/2] | |
Coxeter plane | D6 | D5 |
Graph | ||
Dihedral symmetry | [10] | [8] |
Coxeter plane | D4 | D3 |
Graph | ||
Dihedral symmetry | [6] | [4] |
Coxeter plane | A5 | A3 |
Graph | ||
Dihedral symmetry | [6] | [4] |
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 | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 34560 |
Vertices | 11520 |
Vertex figure | |
Coxeter groups | D6, [33,1,1] |
Properties | convex |
The Cartesian coordinates for the vertices of a Steriruncicantitruncated demihexeract centered at the origin are coordinate permutations:
with an odd number of plus signs.
Coxeter plane | B6 | |
---|---|---|
Graph | ||
Dihedral symmetry | [12/2] | |
Coxeter plane | D6 | D5 |
Graph | ||
Dihedral symmetry | [10] | [8] |
Coxeter plane | D4 | D3 |
Graph | ||
Dihedral symmetry | [6] | [4] |
Coxeter plane | A5 | A3 |
Graph | ||
Dihedral symmetry | [6] | [4] |
There are 47 uniform polytopes with D6 symmetry, 31 are shared by the BC6 symmetry, and 16 are unique:
t0(131) |
t0,1(131) |
t0,2(131) |
t0,3(131) |
t0,4(131) |
t0,1,2(131) |
t0,1,3(131) |
t0,1,4(131) |
t0,2,3(131) |
t0,2,4(131) |
t0,3,4(131) |
t0,1,2,3(131) |
t0,1,2,4(131) |
t0,1,3,4(131) |
t0,2,3,4(131) |
t0,1,2,3,4(131) |
Family | An | BCn | Dn | E6 / E7 / E8 / F4 / G2 | Hn | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Regular polygon | Triangle | Square | Hexagon | Pentagon | ||||||||
Uniform polyhedron | Tetrahedron | Octahedron • Cube | Demicube | Dodecahedron • Icosahedron | ||||||||
Uniform polychoron | 5-cell | 16-cell • Tesseract | Demitesseract | 24-cell | 120-cell • 600-cell | |||||||
Uniform 5-polytope | 5-simplex | 5-orthoplex • 5-cube | 5-demicube | |||||||||
Uniform 6-polytope | 6-simplex | 6-orthoplex • 6-cube | 6-demicube | 122 • 221 | ||||||||
Uniform 7-polytope | 7-simplex | 7-orthoplex • 7-cube | 7-demicube | 132 • 231 • 321 | ||||||||
Uniform 8-polytope | 8-simplex | 8-orthoplex • 8-cube | 8-demicube | 142 • 241 • 421 | ||||||||
Uniform 9-polytope | 9-simplex | 9-orthoplex • 9-cube | 9-demicube | |||||||||
Uniform 10-polytope | 10-simplex | 10-orthoplex • 10-cube | 10-demicube | |||||||||
n-polytopes | n-simplex | n-orthoplex • n-cube | n-demicube | 1k2 • 2k1 • k21 | pentagonal polytope | |||||||
Topics: Polytope families • Regular polytope • List of regular polytopes |