Cantitruncated 120-cell

From Wikipedia, the free encyclopedia

Cantitruncated 120-cell
Close up of Schlegel diagram centered on great rhombicosidodecahedron cell with decagonal faces hidden.
Type	Uniform polychoron
Cells	1920 total: 120 (4.6.10) 1200 (3.4.4) 600 (3.6.6)
Faces	9120: 2400{3}+3600{4}+ 2400{6}+720{10}
Edges	14400
Vertices	7200
Vertex figure	-
Schläfli symbol	t_0,1,2{5,3,3}
Symmetry group	H₄, [3,3,5]
Properties	convex

In geometry, the cantitruncated 120-cell is a uniform polychoron.

This polychoron is related to the regular 120-cell. The cantitruncation operation create new truncated tetrahedral cells at the vertices, and triangular prisms at the edges. The original dodecahedron cells are cantitruncated into great rhombicosidodecahedron cells.

The image shows the polychoron drawn as a Schlegel diagram which projects the 4 dimensional figure into 3-space, distorting the sizes of the cells. In addition, the decagonal faces are hidden, allowing us to see the elemented projected inside.

[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