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Truncated 5-cubes
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In five-dimensional geometry, a truncated 5-cube is a convex uniform 5-polytope, being a truncation of the regular 5-cube.
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.
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Truncated 5-cube
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Truncated 5-cube | ||
---|---|---|
Type | uniform 5-polytope | |
Schläfli symbol | t{4,3,3,3} | |
Coxeter-Dynkin diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4-faces | 42 | 10 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 32 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Cells | 200 | 40 ![]() ![]() ![]() ![]() ![]() ![]() 160 ![]() ![]() ![]() ![]() ![]() ![]() |
Faces | 400 | 80 ![]() ![]() ![]() ![]() 320 ![]() ![]() ![]() ![]() |
Edges | 400 | 80 ![]() 320 ![]() |
Vertices | 160 | |
Vertex figure | ![]() ( )v{3,3} | |
Coxeter group | B5, [3,3,3,4], order 3840 | |
Properties | convex |
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:
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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.
Related polytopes
The truncated 5-cube, is fourth in a sequence of truncated hypercubes:
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Bitruncated 5-cube
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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
Related polytopes
The bitruncated 5-cube is third in a sequence of bitruncated hypercubes:
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Related polytopes
This polytope is one of 31 uniform 5-polytope generated from the regular 5-cube or 5-orthoplex.
Notes
References
External links
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