- Source: Truncated 6-cubes
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.
Truncated 6-cube
= Alternate names
=Truncated hexeract (Acronym: tox) (Jonathan Bowers)
= Construction and coordinates
=The truncated 6-cube may be constructed by truncating the vertices of the 6-cube at
1
/
(
2
+
2
)
{\displaystyle 1/({\sqrt {2}}+2)}
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:
(
±
1
,
±
(
1
+
2
)
,
±
(
1
+
2
)
,
±
(
1
+
2
)
,
±
(
1
+
2
)
,
±
(
1
+
2
)
)
{\displaystyle \left(\pm 1,\ \pm (1+{\sqrt {2}}),\ \pm (1+{\sqrt {2}}),\ \pm (1+{\sqrt {2}}),\ \pm (1+{\sqrt {2}}),\ \pm (1+{\sqrt {2}})\right)}
= Images
== Related polytopes
=The truncated 6-cube, is fifth in a sequence of truncated hypercubes:
Bitruncated 6-cube
= Alternate names
=Bitruncated hexeract (Acronym: botox) (Jonathan Bowers)
= Construction and coordinates
=The Cartesian coordinates of the vertices of a bitruncated 6-cube having edge length 2 are the permutations of:
(
0
,
±
1
,
±
2
,
±
2
,
±
2
,
±
2
)
{\displaystyle \left(0,\ \pm 1,\ \pm 2,\ \pm 2,\ \pm 2,\ \pm 2\right)}
= Images
== Related polytopes
=The bitruncated 6-cube is fourth in a sequence of bitruncated hypercubes:
Tritruncated 6-cube
= Alternate names
=Tritruncated hexeract (Acronym: xog) (Jonathan Bowers)
= Construction and coordinates
=The Cartesian coordinates of the vertices of a tritruncated 6-cube having edge length 2 are the permutations of:
(
0
,
0
,
±
1
,
±
2
,
±
2
,
±
2
)
{\displaystyle \left(0,\ 0,\ \pm 1,\ \pm 2,\ \pm 2,\ \pm 2\right)}
= Images
=Related polytopes
Related polytopes
These polytopes are from a set of 63 Uniform 6-polytopes generated from the B6 Coxeter plane, including the regular 6-cube or 6-orthoplex.
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. "6D uniform polytopes (polypeta)". o3o3o3o3x4x - tox, o3o3o3x3x4o - botox, o3o3x3x3o4o - xog
External links
Weisstein, Eric W. "Hypercube". MathWorld.
Polytopes of Various Dimensions
Multi-dimensional Glossary
Kata Kunci Pencarian:
- Daftar bentuk matematika
- Truncated 6-cubes
- Truncated cube
- Truncated 8-cubes
- Truncated cuboctahedron
- Runcinated 6-cubes
- Truncated 7-cubes
- Truncated tesseract
- Truncated 5-cubes
- Stericated 6-cubes
- List of mathematical shapes
