Surf Wiki
Save to docs
general/5-polytopes

From Surf Wiki (app.surf) — the open knowledge base

D5 polytope

[[File:5-demicube t0 D5.svg160px]][5-demicube](5-demicube)[[File:5-cube t4 B4.svg160px]][5-orthoplex](5-orthoplex)

In 5-dimensional geometry, there are 23 uniform polytopes with D5 symmetry, 8 are unique, and 15 are shared with the B5 symmetry. There are two special forms, the 5-orthoplex, and 5-demicube with 10 and 16 vertices respectively.

They can be visualized as symmetric orthographic projections in Coxeter planes of the D5 Coxeter group, and other subgroups. TOC

Graphs

Symmetric orthographic projections of these 8 polytopes can be made in the D5, D4, D3, A3, Coxeter planes. Ak has [k+1] symmetry, Dk has [2(k-1)] symmetry. The B5 plane is included, with only half the [10] symmetry displayed.

These 8 polytopes are each shown in these 5 symmetry planes, with vertices and edges drawn, and vertices colored by the number of overlapping vertices in each projective position.

#Coxeter plane projectionsCoxeter diagram = Schläfli symbolJohnson and Bowers names[10/2][8][6][4][4]B5D5D4D3A312345678
[[File:5-demicube t0 B5.svg80px]][[File:5-demicube t0 D5.svg80px]][[File:5-demicube t0 D4.svg80px]][[File:5-demicube t0 D3.svg80px]][[File:5-demicube t0 A3.svg80px]]= h{4,3,3,3}[5-demicube](5-demicube)Hemipenteract (hin)
[[File:5-demicube t01 B5.svg80px]][[File:5-demicube t01 D5.svg80px]][[File:5-demicube t01 D4.svg80px]][[File:5-demicube t01 D3.svg80px]][[File:5-demicube t01 A3.svg80px]]= h2{4,3,3,3}Cantic 5-cubeTruncated hemipenteract (thin)
[[File:5-demicube t02 B5.svg80px]][[File:5-demicube t02 D5.svg80px]][[File:5-demicube t02 D4.svg80px]][[File:5-demicube t02 D3.svg80px]][[File:5-demicube t02 A3.svg80px]]= h3{4,3,3,3}Runcic 5-cubeSmall rhombated hemipenteract (sirhin)
[[File:5-demicube t03 B5.svg80px]][[File:5-demicube t03 D5.svg80px]][[File:5-demicube t03 D4.svg80px]][[File:5-demicube t03 D3.svg80px]][[File:5-demicube t03 A3.svg80px]]= h4{4,3,3,3}Steric 5-cubeSmall prismated hemipenteract (siphin)
[[File:5-demicube t012 B5.svg80px]][[File:5-demicube t012 D5.svg80px]][[File:5-demicube t012 D4.svg80px]][[File:5-demicube t012 D3.svg80px]][[File:5-demicube t012 A3.svg80px]]= h2,3{4,3,3,3}Runcicantic 5-cubeGreat rhombated hemipenteract (girhin)
[[File:5-demicube t013 B5.svg80px]][[File:5-demicube t013 D5.svg80px]][[File:5-demicube t013 D4.svg80px]][[File:5-demicube t013 D3.svg80px]][[File:5-demicube t013 A3.svg80px]]= h2,4{4,3,3,3}Stericantic 5-cubePrismatotruncated hemipenteract (pithin)
[[File:5-demicube t023 B5.svg80px]][[File:5-demicube t023 D5.svg80px]][[File:5-demicube t023 D4.svg80px]][[File:5-demicube t023 D3.svg80px]][[File:5-demicube t023 A3.svg80px]]= h3,4{4,3,3,3}Steriruncic 5-cubePrismatorhombated hemipenteract (pirhin)
[[File:5-demicube t0123 B5.svg80px]][[File:5-demicube t0123 D5.svg80px]][[File:5-demicube t0123 D4.svg80px]][[File:5-demicube t0123 D3.svg80px]][[File:5-demicube t0123 A3.svg80px]]= h2,3,4{4,3,3,3}Steriruncicantic 5-cubeGreat prismated hemipenteract (giphin)

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,
    • (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]
  • N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. Dissertation, University of Toronto, 1966

Notes

References

  1. "Wiley::Kaleidoscopes: Selected Writings of H.S.M. Coxeter".
Info: Wikipedia Source

This article was imported from Wikipedia and is available under the Creative Commons Attribution-ShareAlike 4.0 License. Content has been adapted to SurfDoc format. Original contributors can be found on the article history page.

5-polytopes
Want to explore this topic further?

Ask Mako anything about D5 polytope — get instant answers, deeper analysis, and related topics.

Research with Mako

Free with your Surf account

Content sourced from Wikipedia, available under CC BY-SA 4.0.

This content may have been generated or modified by AI. CloudSurf Software LLC is not responsible for the accuracy, completeness, or reliability of AI-generated content. Always verify important information from primary sources.

Report