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In five-dimensional geometry, a stericated 5-cube is a convex uniform 5-polytope with fourth-order truncations (sterication) of the regular 5-cube.
5-cube |
Stericated 5-cube |
Steritruncated 5-cube |
Stericantellated 5-cube |
Steritruncated 5-orthoplex |
Stericantitruncated 5-cube |
Steriruncitruncated 5-cube |
Stericantitruncated 5-orthoplex |
Omnitruncated 5-cube |
Orthogonal projections in B5 Coxeter plane |
---|
There are eight degrees of sterication for the 5-cube, including permutations of runcination, cantellation, and truncation. The simple stericated 5-cube is also called an expanded 5-cube, with the first and last nodes ringed, for being constructible by an expansion operation applied to the regular 5-cube. The highest form, the sterirunci
Stericated 5-cube | ||
Type | Uniform 5-polytope | |
Schläfli symbol | 2r2r{4,3,3,3} | |
Coxeter-Dynkin diagram | ||
4-faces | 242 | |
Cells | 800 | |
Faces | 1040 | |
Edges | 640 | |
Vertices | 160 | |
Vertex figure | ||
Coxeter group | B5 [4,3,3,3] | |
Properties | convex |
The Cartesian coordinates of the vertices of a stericated 5-cube having edge length 2 are all permutations of:
The stericated 5-cube is constructed by a sterication operation applied to the 5-cube.
The stericated 5-cube can be dissected into two tesseractic cupolae and a runcinated tesseract between them. This dissection can be seen as analogous to the 4D runcinated tesseract being dissected into two cubic cupolae and a central rhombicuboctahedral prism between them, and also the 3D rhombicuboctahedron being dissected into two square cupolae with a central octagonal prism between them.
Coxeter plane | B5 | B4 / D5 | B3 / D4 / A2 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [10] | [8] | [6] |
Coxeter plane | B2 | A3 | |
Graph | |||
Dihedral symmetry | [4] | [4] |
Steritruncated 5-cube | |
---|---|
Type | uniform 5-polytope |
Schläfli symbol | t0,1,4{4,3,3,3} |
Coxeter-Dynkin diagrams | |
4-faces | 242 |
Cells | 1600 |
Faces | 2960 |
Edges | 2240 |
Vertices | 640 |
Vertex figure | |
Coxeter groups | B5, [3,3,3,4] |
Properties | convex |
The Cartesian coordinates of the vertices of a steritruncated 5-cube having edge length 2 are all permutations of:
Coxeter plane | B5 | B4 / D5 | B3 / D4 / A2 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [10] | [8] | [6] |
Coxeter plane | B2 | A3 | |
Graph | |||
Dihedral symmetry | [4] | [4] |
Stericantellated 5-cube | ||
Type | Uniform 5-polytope | |
Schläfli symbol | t0,2,4{4,3,3,3} | |
Coxeter-Dynkin diagram | ||
4-faces | 242 | |
Cells | 2080 | |
Faces | 4720 | |
Edges | 3840 | |
Vertices | 960 | |
Vertex figure | ||
Coxeter group | B5 [4,3,3,3] | |
Properties | convex |
The Cartesian coordinates of the vertices of a stericantellated 5-cube having edge length 2 are all permutations of:
Coxeter plane | B5 | B4 / D5 | B3 / D4 / A2 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [10] | [8] | [6] |
Coxeter plane | B2 | A3 | |
Graph | |||
Dihedral symmetry | [4] | [4] |
Stericantitruncated 5-cube | ||
Type | Uniform 5-polytope | |
Schläfli symbol | t0,1,2,4{4,3,3,3} | |
Coxeter-Dynkin diagram |
||
4-faces | 242 | |
Cells | 2400 | |
Faces | 6000 | |
Edges | 5760 | |
Vertices | 1920 | |
Vertex figure | ||
Coxeter group | B5 [4,3,3,3] | |
Properties | convex, isogonal |
The Cartesian coordinates of the vertices of a stericantitruncated 5-cube having an edge length of 2 are given by all permutations of coordinates and sign of:
Coxeter plane | B5 | B4 / D5 | B3 / D4 / A2 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [10] | [8] | [6] |
Coxeter plane | B2 | A3 | |
Graph | |||
Dihedral symmetry | [4] | [4] |
Steriruncitruncated 5-cube | ||
Type | Uniform 5-polytope | |
Schläfli symbol | 2t2r{4,3,3,3} | |
Coxeter-Dynkin diagram |
||
4-faces | 242 | |
Cells | 2160 | |
Faces | 5760 | |
Edges | 5760 | |
Vertices | 1920 | |
Vertex figure | ||
Coxeter group | B5 [4,3,3,3] | |
Properties | convex, isogonal |
The Cartesian coordinates of the vertices of a steriruncitruncated penteract having an edge length of 2 are given by all permutations of coordinates and sign of:
Coxeter plane | B5 | B4 / D5 | B3 / D4 / A2 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [10] | [8] | [6] |
Coxeter plane | B2 | A3 | |
Graph | |||
Dihedral symmetry | [4] | [4] |
Steritruncated 5-orthoplex | |
---|---|
Type | uniform 5-polytope |
Schläfli symbol | t0,1,4{3,3,3,4} |
Coxeter-Dynkin diagrams | |
4-faces | 242 |
Cells | 1520 |
Faces | 2880 |
Edges | 2240 |
Vertices | 640 |
Vertex figure | |
Coxeter group | B5, [3,3,3,4] |
Properties | convex |
Cartesian coordinates for the vertices of a steritruncated 5-orthoplex, centered at the origin, are all permutations of
Coxeter plane | B5 | B4 / D5 | B3 / D4 / A2 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [10] | [8] | [6] |
Coxeter plane | B2 | A3 | |
Graph | |||
Dihedral symmetry | [4] | [4] |
Stericantitruncated 5-orthoplex | ||
Type | Uniform 5-polytope | |
Schläfli symbol | t0,2,3,4{4,3,3,3} | |
Coxeter-Dynkin diagram |
||
4-faces | 242 | |
Cells | 2320 | |
Faces | 5920 | |
Edges | 5760 | |
Vertices | 1920 | |
Vertex figure | ||
Coxeter group | B5 [4,3,3,3] | |
Properties | convex, isogonal |
The Cartesian coordinates of the vertices of a stericantitruncated 5-orthoplex having an edge length of 2 are given by all permutations of coordinates and sign of:
Coxeter plane | B5 | B4 / D5 | B3 / D4 / A2 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [10] | [8] | [6] |
Coxeter plane | B2 | A3 | |
Graph | |||
Dihedral symmetry | [4] | [4] |
Omnitruncated 5-cube | ||
Type | Uniform 5-polytope | |
Schläfli symbol | tr2r{4,3,3,3} | |
Coxeter-Dynkin diagram |
||
4-faces | 242 | |
Cells | 2640 | |
Faces | 8160 | |
Edges | 9600 | |
Vertices | 3840 | |
Vertex figure | irr. {3,3,3} | |
Coxeter group | B5 [4,3,3,3] | |
Properties | convex, isogonal |
The Cartesian coordinates of the vertices of an omnitruncated 5-cube having an edge length of 2 are given by all permutations of coordinates and sign of:
Coxeter plane | B5 | B4 / D5 | B3 / D4 / A2 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [10] | [8] | [6] |
Coxeter plane | B2 | A3 | |
Graph | |||
Dihedral symmetry | [4] | [4] |
The full snub 5-cube or omnisnub 5-cube, defined as an alternation of the omnitruncated 5-cube is not uniform, but it can be given Coxeter diagram and symmetry [4,3,3,3]+, and constructed from 10 snub tesseracts, 32 snub 5-cells, 40 snub cubic antiprisms, 80 snub tetrahedral antiprisms, 80 3-4 duoantiprisms, and 1920 irregular 5-cells filling the gaps at the deleted vertices.
This polytope is one of 31 uniform 5-polytopes generated from the regular 5-cube or 5-orthoplex.
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