- Source: Truncated 5-cubes
In five-dimensional geometry, a 5.180.24.3/info/truncated" target="_blank">truncated 5-cube is a convex uniform 5-polytope, being a truncation of the regular 5-cube.
There are four unique truncations of the 5-cube. Vertices of the 5.180.24.3/info/truncated" target="_blank">truncated 5-cube are located as pairs on the edge of the 5-cube. Vertices of the bitruncated 5-cube are located on the square faces of the 5-cube. The third and fourth truncations are more easily constructed as second and first truncations of the 5-orthoplex.
5.180.24.3/info/truncated" target="_blank">Truncated 5-cube
= Alternate names
=5.180.24.3/info/truncated" target="_blank">Truncated penteract (Acronym: tan) (Jonathan Bowers)
= Construction and coordinates
=The 5.180.24.3/info/truncated" target="_blank">truncated 5-cube may be constructed by truncating the vertices of the 5-cube at
1
/
(
2
+
2
)
{\displaystyle 1/({\sqrt {2}}+2)}
of the edge length. A regular 5-cell is formed at each 5.180.24.3/info/truncated" target="_blank">truncated vertex.
The Cartesian coordinates of the vertices of a 5.180.24.3/info/truncated" target="_blank">truncated 5-cube having edge length 2 are all permutations of:
(
±
1
,
±
(
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}})\right)}
= Images
=The 5.180.24.3/info/truncated" target="_blank">truncated 5-cube is constructed by a truncation applied to the 5-cube. All edges are shortened, and two new vertices are added on each original edge.
= Related polytopes
=The 5.180.24.3/info/truncated" target="_blank">truncated 5-cube, is fourth in a sequence of 5.180.24.3/info/truncated" target="_blank">truncated hypercubes:
Bitruncated 5-cube
= Alternate names
=Bitruncated penteract (Acronym: bittin) (Jonathan Bowers)
= Construction and coordinates
=The bitruncated 5-cube may be constructed by bitruncating the vertices of the 5-cube at
2
{\displaystyle {\sqrt {2}}}
of the edge length.
The Cartesian coordinates of the vertices of a bitruncated 5-cube having edge length 2 are all permutations of:
(
0
,
±
1
,
±
2
,
±
2
,
±
2
)
{\displaystyle \left(0,\ \pm 1,\ \pm 2,\ \pm 2,\ \pm 2\right)}
= Images
== Related polytopes
=The bitruncated 5-cube is third in a sequence of bitruncated hypercubes:
Related polytopes
This polytope is one of 31 uniform 5-polytope generated from the regular 5-cube or 5-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. "5D uniform polytopes (polytera)". o3o3o3x4x - tan, o3o3x3x4o - bittin
External links
Polytopes of Various Dimensions
Multi-dimensional Glossary
Kata Kunci Pencarian:
- Daftar bentuk matematika
- Truncated cube
- Truncated 5-cubes
- Truncated 8-cubes
- Truncated 6-cubes
- Truncated 7-cubes
- Truncated tesseract
- Truncated cuboctahedron
- List of mathematical shapes
- List of polygons, polyhedra and polytopes
- Truncated 5-orthoplexes
