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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.
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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.
Alternate names
Construction and coordinates
The truncated 5-cube may be constructed by truncating the vertices of the 5-cube at
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.
Related polytopes
The truncated 5-cube, is fourth in a sequence of truncated hypercubes:
Alternate names
Construction and coordinates
The bitruncated 5-cube may be constructed by bitruncating the vertices of the 5-cube at
The Cartesian coordinates of the vertices of a bitruncated 5-cube having edge length 2 are all permutations of:
Related polytopes
The bitruncated 5-cube is third in a sequence of bitruncated hypercubes:
Related polytopes
This polytope is one of 31 uniform 5-polytope generated from the regular 5-cube or 5-orthoplex.