Truncated 6-orthoplexes
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Orthogonal projections in B6 Coxeter plane |
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In six-dimensional geometry, a truncated 6-orthoplex is a convex uniform 6-polytope, being a truncation of the regular 6-orthoplex.
There are 5 degrees of truncation for the 6-orthoplex. Vertices of the truncated 6-orthoplex are located as pairs on the edge of the 6-orthoplex. Vertices of the bitruncated 6-orthoplex are located on the triangular faces of the 6-orthoplex. Vertices of the tritruncated 6-orthoplex are located inside the tetrahedral cells of the 6-orthoplex. {{-}}
Truncated 6-orthoplex
Truncated 6-orthoplex |
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Type |
Schläfli symbol |
Coxeter-Dynkin diagrams |
5-faces |
4-faces |
Cells |
Faces |
Edges |
Vertices |
Vertex figure |
Coxeter groups |
Properties |
Alternate names
- Truncated hexacross
- Truncated hexacontatetrapeton (Acronym: tag) (Jonathan Bowers)
Construction
There are two Coxeter groups associated with the truncated hexacross, one with the C6 or [4,3,3,3,3] Coxeter group, and a lower symmetry with the D6 or [33,1,1] Coxeter group.
Coordinates
Cartesian coordinates for the vertices of a truncated 6-orthoplex, centered at the origin, are all 120 vertices are sign (4) and coordinate (30) permutations of
- (±2,±1,0,0,0,0)
Images
Bitruncated 6-orthoplex
Bitruncated 6-orthoplex |
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Type |
Schläfli symbol |
Coxeter-Dynkin diagrams |
5-faces |
4-faces |
Cells |
Faces |
Edges |
Vertices |
Vertex figure |
Coxeter groups |
Properties |
Alternate names
- Bitruncated hexacross
- Bitruncated hexacontatetrapeton (Acronym: botag) (Jonathan Bowers)
Images
Related polytopes
These polytopes are in a set of 63 uniform 6-polytopes generated from the B6 Coxeter plane, including the regular 6-cube and 6-orthoplex.
References
- H.S.M. Coxeter:
- H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973
- Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivić Weiss, Wiley-Interscience Publication, 1995, wiley.com,
- (Paper 22) H.S.M. Coxeter, Regular and Semi-Regular Polytopes I, [Math. Zeit. 46 (1940) 380–407, MR 2,10]
- (Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559–591]
- (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3–45]
- Norman Johnson Uniform Polytopes, Manuscript (1991)
- N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D.
x3x3o3o3o4o - tag, o3x3x3o3o4o - botag