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Steric 5-cubes

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Steric 5-cubes
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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.

More information Orthogonal projections in B5 Coxeter plane ...
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Steric 5-cube

Steric 5-cube
Typeuniform polyteron
Schläfli symbol
  • t0,3{3,32,1}
  • h4{4,3,3,3
}
Coxeter-Dynkin diagram
4-faces82
Cells480
Faces720
Edges400
Vertices80
Vertex figure{3,3}-t1{3,3} antiprism
Coxeter groupsD5, [32,1,1]
Propertiesconvex

Alternate names

  • Steric penteract, runcinated demipenteract
  • Small prismated hemipenteract (siphin) (Jonathan Bowers)[1]:(x3o3o *b3o3x - siphin)

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.

Images

More information Coxeter plane, B5 ...
More information Dimensional family of steric n-cubes, n ...
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Stericantic 5-cube

More information Stericantic 5-cube ...

Alternate names

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.

Images

More information Coxeter plane, B5 ...
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Steriruncic 5-cube

More information Steriruncic 5-cube ...

Alternate names

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.

Images

More information Coxeter plane, B5 ...

Steriruncicantic 5-cube

More information Steriruncicantic 5-cube ...

Alternate names

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.

Images

More information Coxeter plane, B5 ...
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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.

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References

Further reading

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