Top Qs
Timeline
Chat
Perspective
Truncated 6-cubes
From Wikipedia, the free encyclopedia
Remove ads
In six-dimensional geometry, a truncated 6-cube (or truncated hexeract) is a convex uniform 6-polytope, being a truncation of the regular 6-cube.
There are 5 truncations for the 6-cube. Vertices of the truncated 6-cube are located as pairs on the edge of the 6-cube. Vertices of the bitruncated 6-cube are located on the square faces of the 6-cube. Vertices of the tritruncated 6-cube are located inside the cubic cells of the 6-cube.
Remove ads
Truncated 6-cube
Summarize
Perspective
Truncated 6-cube | |
---|---|
Type | uniform 6-polytope |
Class | B6 polytope |
Schläfli symbol | t{4,3,3,3,3} |
Coxeter-Dynkin diagrams | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
5-faces | 76 |
4-faces | 464 |
Cells | 1120 |
Faces | 1520 |
Edges | 1152 |
Vertices | 384 |
Vertex figure | ![]() ( )v{3,3,3} |
Coxeter groups | B6, [3,3,3,3,4] |
Properties | convex |
Alternate names
- Truncated hexeract (Acronym: tox) (Jonathan Bowers)[1]
Construction and coordinates
The truncated 6-cube may be constructed by truncating the vertices of the 6-cube at of the edge length. A regular 5-simplex replaces each original vertex.
The Cartesian coordinates of the vertices of a truncated 6-cube having edge length 2 are the permutations of:
Images
Related polytopes
The truncated 6-cube, is fifth in a sequence of truncated hypercubes:
Remove ads
Bitruncated 6-cube
Summarize
Perspective
Alternate names
- Bitruncated hexeract (Acronym: botox) (Jonathan Bowers)[2]
Construction and coordinates
The Cartesian coordinates of the vertices of a bitruncated 6-cube having edge length 2 are the permutations of:
Images
Related polytopes
The bitruncated 6-cube is fourth in a sequence of bitruncated hypercubes:
Remove ads
Tritruncated 6-cube
Summarize
Perspective
Alternate names
- Tritruncated hexeract (Acronym: xog) (Jonathan Bowers)[4]
Construction and coordinates
The Cartesian coordinates of the vertices of a tritruncated 6-cube having edge length 2 are the permutations of:
Images
Related polytopes
The table below contains a set of 63 Uniform 6-polytopes generated from the B6 Coxeter plane, including the regular 6-cube or 6-orthoplex.
Remove ads
Notes
References
External links
Wikiwand - on
Seamless Wikipedia browsing. On steroids.
Remove ads