• Source: Truncated 7-cubes

In seven-dimensional geometry, a truncated 7-cube is a convex uniform 7-polytope, being a truncation of the regular 7-cube.
There are 6 truncations for the 7-cube. Vertices of the truncated 7-cube are located as pairs on the edge of the 7-cube. Vertices of the bitruncated 7-cube are located on the square faces of the 7-cube. Vertices of the tritruncated 7-cube are located inside the cubic cells of the 7-cube. The final three truncations are best expressed relative to the 7-orthoplex.




Truncated 7-cube






= Alternate names

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Truncated hepteract (Jonathan Bowers)




= Coordinates

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Cartesian coordinates for the vertices of a truncated 7-cube, centered at the origin, are all sign and coordinate permutations of

(1,1+√2,1+√2,1+√2,1+√2,1+√2,1+√2)




= Images

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= Related polytopes

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The truncated 7-cube, is sixth in a sequence of truncated hypercubes:




Bitruncated 7-cube






= Alternate names

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Bitruncated hepteract (Jonathan Bowers)




= Coordinates

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Cartesian coordinates for the vertices of a bitruncated 7-cube, centered at the origin, are all sign and coordinate permutations of

(±2,±2,±2,±2,±2,±1,0)




= Images

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= Related polytopes

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The bitruncated 7-cube is fifth in a sequence of bitruncated hypercubes:




Tritruncated 7-cube






= Alternate names

=
Tritruncated hepteract (Jonathan Bowers)




= Coordinates

=
Cartesian coordinates for the vertices of a tritruncated 7-cube, centered at the origin, are all sign and coordinate permutations of

(±2,±2,±2,±2,±1,0,0)




= Images

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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. "7D uniform polytopes (polyexa)". o3o3o3o3o3x4x - taz, o3o3o3o3x3x4o - botaz, o3o3o3x3x3o4o - totaz




External links


Polytopes of Various Dimensions
Multi-dimensional Glossary

Kata Kunci Pencarian:

• Daftar bentuk matematika
• Truncated 7-cubes
• Truncated cube
• Truncated 8-cubes
• Truncated 6-cubes
• Truncated 5-cubes
• Stericated 7-cubes
• Pentellated 7-cubes
• Hexicated 7-cubes
• Truncated tesseract
• List of polygons, polyhedra and polytopes