Rectified 600-cell

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Rectified 600-cell

Type	Uniform polychoron
Cells	600 (3.3.3.3) 120 (3.3.3.3.3)
Faces	3600 {3}
Edges	3600
Vertices	720
Vertex figure	5 (3.3.3.3) 2 (3.3.3.3.3) (pentagonal prism)
Schläfli symbol	t₁{3,3,5}
Symmetry group	H₄ or [3,3,5]
Properties	convex

Vertex figure: pentagonal prism
7 faces:

5 (3.3.3.3) and 2 (3.3.3.3.3)

An orthographic projection

In geometry, the rectified 600-cell is a convex uniform polychoron composed of 600 regular octahedra and 120 icosahedra cells. Each edge has two octahedra and one icosahedron. Each vertex has five octahedra and two icosahedra. In total it has 3600 triangle faces, 3600 edges, and 720 vertices.

It is one of three semiregular polychora made of two or more cells which are platonic solids, discovered by Thorold Gosset in his 1900 paper. He called it a octicosahedric for being made of octahedron and icosahedron cells.

Containing the cell realms of both the regular 120-cell and the regular 600-cell, it can be considered analogous to the polyhedron icosidodecahedron, which is a rectified icosahedron and rectified dodecahedron.

Names:

Icosahedral hexacosihecatonicosachoron
Rectified 600-cell (Norman W. Johnson)
Rectified hexacosichoron
Rectified polytetrahedron
Rox (Jonathan Bowers)

The vertex figure of the rectified 600-cell is a regular pentagonal prism.

[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