5-cubeOrthogonal projections in B Coxeter plane
In five-dimensional geometry, a steric 5-cube, 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 Steric 5-cubeTypeuniform polyteronSchläfli symbol Coxeter-Dynkin diagram4-faces82Cells480Faces720Edges400Vertices80Vertex figure{3,3}-t{3,3} antiprismCoxeter groupsD, Propertiesconvex
Alternate names Steric penteract, runcinated demipenteract Small prismated hemipenteract (siphin) (Jonathan Bowers)
Cartesian coordinates The Cartesian coordinates for the 80 vertices of a steric 5-cube centered at the origin are the permutations of (±1,±1,±1,±1,±3) with an odd number of plus signs.
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Related polytopes
Stericantic 5-cube Stericantic 5-cubeTypeuniform polyteronSchläfli symbol Coxeter-Dynkin diagram4-faces82Cells720Faces1840Edges1680Vertices480Vertex figureCoxeter groupsD, Propertiesconvex
Alternate names Prismatotruncated hemipenteract (pithin) (Jonathan Bowers)
Cartesian coordinates The Cartesian coordinates for the 480 vertices of a stericantic 5-cube centered at the origin are coordinate permutations: (±1,±1,±3,±3,±5) with an odd number of plus signs.
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Steriruncic 5-cube Steriruncic 5-cubeTypeuniform polyteronSchläfli symbol Coxeter-Dynkin diagram4-faces82Cells560Faces1280Edges1120Vertices320Vertex figureCoxeter groupsD, Propertiesconvex
Alternate names Prismatorhombated hemipenteract (pirhin) (Jonathan Bowers)
Cartesian coordinates The Cartesian coordinates for the 320 vertices of a steriruncic 5-cube centered at the origin are coordinate permutations: (±1,±1,±1,±3,±5) with an odd number of plus signs.
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Steriruncicantic 5-cube Steriruncicantic 5-cubeTypeuniform polyteronSchläfli symbol Coxeter-Dynkin diagram4-faces82Cells720Faces2080Edges2400Vertices960Vertex figureCoxeter groupsD, Propertiesconvex
Alternate names Great prismated hemipenteract (giphin) (Jonathan Bowers)
Cartesian coordinates The Cartesian coordinates for the 960 vertices of a steriruncicantic 5-cube centered at the origin are coordinate permutations: (±1,±1,±3,±5,±7) with an odd number of plus signs.
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Related polytopes These polytopes are based on the 5-demicube, a member of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family.
There are 23 uniform polytera (uniform 5-polytopes) that can be constructed from the D symmetry of the 5-demicube, 8 of which are unique to this family, and 15 are shared within the 5-cube family.
References
Further reading
External links
Polytopes of Various Dimensions Multi-dimensional Glossary