- Source: Truncated 8-cubes
In eight-dimensional geometry, a truncated 8-cube is a convex uniform 8-polytope, being a truncation of the regular 8-cube.
There are unique 7 degrees of truncation for the 8-cube. Vertices of the truncation 8-cube are located as pairs on the edge of the 8-cube. Vertices of the bitruncated 8-cube are located on the square faces of the 8-cube. Vertices of the tritruncated 7-cube are located inside the cubic cells of the 8-cube. The final truncations are best expressed relative to the 8-orthoplex.
Truncated 8-cube
= Alternate names
=Truncated octeract (acronym tocto) (Jonathan Bowers)
= Coordinates
=Cartesian coordinates for the vertices of a truncated 8-cube, centered at the origin, are all 224 vertices are sign (4) and coordinate (56) permutations of
(±2,±2,±2,±2,±2,±2,±1,0)
= Images
== Related polytopes
=The truncated 8-cube, is seventh in a sequence of truncated hypercubes:
Bitruncated 8-cube
= Alternate names
=Bitruncated octeract (acronym bato) (Jonathan Bowers)
= Coordinates
=Cartesian coordinates for the vertices of a truncated 8-cube, centered at the origin, are all the sign coordinate permutations of
(±2,±2,±2,±2,±2,±1,0,0)
= Images
== Related polytopes
=The bitruncated 8-cube is sixth in a sequence of bitruncated hypercubes:
Tritruncated 8-cube
= Alternate names
=Tritruncated octeract (acronym tato) (Jonathan Bowers)
= Coordinates
=Cartesian coordinates for the vertices of a truncated 8-cube, centered at the origin, are all the sign coordinate permutations of
(±2,±2,±2,±2,±1,0,0,0)
= Images
=Quadritruncated 8-cube
= Alternate names
=Quadritruncated octeract (acronym oke) (Jonathan Bowers)
= Coordinates
=Cartesian coordinates for the vertices of a bitruncated 8-orthoplex, centered at the origin, are all sign and coordinate permutations of
(±2,±2,±2,±2,±1,0,0,0)
= Images
== Related polytopes
=Notes
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 Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 [1]
(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.
Klitzing, Richard. "8D uniform polytopes (polyzetta)". o3o3o3o3o3o3x4x – tocto, o3o3o3o3o3x3x4o – bato, o3o3o3o3x3x3o4o – tato, o3o3o3x3x3o3o4o – oke
External links
Polytopes of Various Dimensions
Multi-dimensional Glossary
Kata Kunci Pencarian:
- Daftar bentuk matematika
- Truncated 8-cubes
- Truncated cube
- Truncated tesseract
- Biaugmented truncated cube
- Truncated cuboctahedron
- Augmented truncated cube
- Truncated 7-cubes
- Truncated 6-cubes
- Truncated 5-cubes
- Truncated 8-orthoplexes
