Truncated 5-cubes

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Truncated 5-cubes

In five-dimensional geometry, a truncated 5-cube is a convex uniform 5-polytope, being a truncation of the regular 5-cube.

More information Orthogonal projections in B5 Coxeter plane ...
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There are four unique truncations of the 5-cube. Vertices of the truncated 5-cube are located as pairs on the edge of the 5-cube. Vertices of the bitruncated 5-cube are located on the square faces of the 5-cube. The third and fourth truncations are more easily constructed as second and first truncations of the 5-orthoplex.

Truncated 5-cube

Summarize
Perspective
Truncated 5-cube
Typeuniform 5-polytope
Schläfli symbolt{4,3,3,3}
Coxeter-Dynkin diagram
4-faces4210
32
Cells20040
160
Faces40080
320
Edges40080
320
Vertices160
Vertex figure
( )v{3,3}
Coxeter groupB5, [3,3,3,4], order 3840
Propertiesconvex

Alternate names

  • Truncated penteract (Acronym: tan) (Jonathan Bowers)

Construction and coordinates

The truncated 5-cube may be constructed by truncating the vertices of the 5-cube at of the edge length. A regular 5-cell is formed at each truncated vertex.

The Cartesian coordinates of the vertices of a truncated 5-cube having edge length 2 are all permutations of:

Images

The truncated 5-cube is constructed by a truncation applied to the 5-cube. All edges are shortened, and two new vertices are added on each original edge.

More information Coxeter plane, B5 ...
orthographic projections
Coxeter plane B5 B4 / D5 B3 / D4 / A2
Graph Thumb Thumb Thumb
Dihedral symmetry [10] [8] [6]
Coxeter plane B2 A3
Graph Thumb Thumb
Dihedral symmetry [4] [4]
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The truncated 5-cube, is fourth in a sequence of truncated hypercubes:

Bitruncated 5-cube

Summarize
Perspective
More information Bitruncated 5-cube ...
Bitruncated 5-cube
Typeuniform 5-polytope
Schläfli symbol2t{4,3,3,3}
Coxeter-Dynkin diagrams
4-faces4210
32
Cells28040
160
80
Faces72080
320
320
Edges800320
480
Vertices320
Vertex figureThumb
{ }v{3}
Coxeter groupsB5, [3,3,3,4], order 3840
Propertiesconvex
Close

Alternate names

  • Bitruncated penteract (Acronym: bittin) (Jonathan Bowers)

Construction and coordinates

The bitruncated 5-cube may be constructed by bitruncating the vertices of the 5-cube at of the edge length.

The Cartesian coordinates of the vertices of a bitruncated 5-cube having edge length 2 are all permutations of:

Images

More information Coxeter plane, B5 ...
orthographic projections
Coxeter plane B5 B4 / D5 B3 / D4 / A2
Graph Thumb Thumb Thumb
Dihedral symmetry [10] [8] [6]
Coxeter plane B2 A3
Graph Thumb Thumb
Dihedral symmetry [4] [4]
Close

The bitruncated 5-cube is third in a sequence of bitruncated hypercubes:

More information Image, Name ...
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This polytope is one of 31 uniform 5-polytope generated from the regular 5-cube or 5-orthoplex.

Notes

References

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