Omnitruncated 120-cell

From Wikipedia, the free encyclopedia

Omnitruncated 120-cell
stereographic projection (centered on truncated icosidodecahedron)
Type	Uniform polychoron
Cells	2640 total: 120 4.6.10 600 4.6.6 720 4.4.10 1200 4.4.6
Faces	17040 total: 10800 {4}, 4800 {6} 1440 {10}
Edges	28800
Vertices	14400
Vertex figure	Chiral scalene tetrahedron
Schläfli symbol	t_0,1,2,3{3,3,5}
Symmetry group	H₄, [3,3,5]
Properties	convex

In geometry, the omnitruncated 120-cell is a convex uniform polychoron composed of 2640 cells: 120 truncated icosidodecahedra, 600 truncated octahedra, 720 decagonal prisms, and 1200 pentagonal prisms.

It also has 14400 vertices, 28800 edges, and 17040 faces, and is the largest convex uniform polychoron.

The vertices and edges form the Cayley graph of the Coxeter group H₄

The first complete physical model of a 3D projection of the omnitruncated 120-cell was built by a team lead by Daniel Duddy and David Richter on Aug. 9th 2006 using the (Zome) system in the London Knowledge Lab for the 2006 Bridges Conference.

1 Alternate names
2 See also
3 References
4 External links

[edit] Alternate names

Omnitruncated 120-cell / Omnitruncated 600-cell (Norman W. Johnson)
Omnitruncated hecatonicosachoron / Omnitruncated hexacosichoron
Omnitruncated polydodecahedron / Omnitruncated polytetrahedron
Great diprismatohexacosihecatonicosachoron (Jonathan Bowers)
- Gidpixhi (for great diprismatohexacosihecatonicosachoron)

[edit] See also

[edit] References

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]
J.H. Conway and M.J.T. Guy: Four-Dimensional Archimedean Polytopes, Proceedings of the Colloquium on Convexity at Copenhagen, page 38 und 39, 1965
N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. Dissertation, University of Toronto, 1966
M. Möller: Definitions and computations to the Platonic and Archimedean polyhedrons, thesis (diploma), University of Hamburg, 2001