Bitruncated_5-cube

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.

More information Orthogonal projections in B5 Coxeter plane ...

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

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

Construction and coordinates

The truncated 5-cube may be constructed by truncating the vertices of the 5-cube at $1/({\sqrt {2}}+2)$ 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:

\left(\pm 1,\ \pm (1+{\sqrt {2}}),\ \pm (1+{\sqrt {2}}),\ \pm (1+{\sqrt {2}}),\ \pm (1+{\sqrt {2}})\right)