Jean-Marc Fontaine

5-cube Template:CDD	Truncated 5-cube Template:CDD	Bitruncated 5-cube Template:CDD
5-orthoplex Template:CDD	Truncated 5-orthoplex Template:CDD	Bitruncated 5-orthoplex Template:CDD
Orthogonal projections in BC5 Coxeter plane

In five-dimensional geometry, a 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 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.

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Truncated 5-cube

Truncated 5-cube
Type	uniform polyteron
Schläfli symbol	t{4,3,3,3}
Coxeter-Dynkin diagrams	Template:CDD
4-faces	42
Cells	200
Faces	400
Edges	400
Vertices	160
Vertex figure	Elongated tetrahedral pyramid
Coxeter groups	BC5, [3,3,3,4]
Properties	convex

Alternate names

• Truncated penteract (Acronym: tan) (Jonathan Bowers)

Construction and coordinates

The truncated 5-cube may be constructed by truncating the vertices of the 5-cube at $1/({\sqrt {2}}+2)$ of the edge length. A regular 5-cell is formed at each truncated vertex.

The Cartesian coordinates of the vertices of a truncated 5-cube having edge length 2 are all permutations of:

$\left(\pm 1,\ \pm (1+{\sqrt {2}}),\ \pm (1+{\sqrt {2}}),\ \pm (1+{\sqrt {2}}),\ \pm (1+{\sqrt {2}})\right)$

Images

The 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 truncated 5-cube, is fourth in a sequence of truncated hypercubes: I just lately had the opportunity to check a plugin referred to as the WooCommerce Reserving and Appointments Plugin from Tyche Softwares. It adds booking and appointment functionality to your WordPress powered web site, and integrates properly with WooCommerce to charge a price for these bookings.

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Bitruncated 5-cube

Bitruncated 5-cube
Type	uniform polyteron
Schläfli symbol	2t{4,3,3,3}
Coxeter-Dynkin diagrams	Template:CDD Template:CDD
4-faces	42
Cells	280
Faces	720
Edges	800
Vertices	320
Vertex figure	Irr. 5-cell
Coxeter groups	BC5, [3,3,3,4]
Properties	convex

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 ${\sqrt {2}}$ of the edge length.

The Cartesian coordinates of the vertices of a bitruncated 5-cube having edge length 2 are all permutations of:

$\left(0,\ \pm 1,\ \pm 2,\ \pm 2,\ \pm 2\right)$

Related polytopes

The bitruncated 5-cube is third in a sequence of bitruncated hypercubes: My name is Margene (46 years old) and my hobbies are Baton twirling and Photography.

my web blog: hombre embarazado (http://Www.Tumaternidad.com)

Related polytopes

This polytope is one of 31 uniform polytera generated from the regular 5-cube or 5-orthoplex.

Notes

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

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, editied 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.
• Template:KlitzingPolytopes o3o3o3x4x - tan, o3o3x3x4o - bittin

External links

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• Template:GlossaryForHyperspace
• Polytopes of Various Dimensions
• Multi-dimensional Glossary