Truncated 120-cell

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Truncated 120-cell
Schlegel diagram (tetrahedron cells visible)
Type	Uniform polychoron
Schläfli symbol	t0,1{5,3,3}
Coxeter-Dynkin diagrams
Cells	600 3.3.3 120 3.10.10
Faces	2400 triangles 720 decagons
Edges	4800
Vertices	2400
Symmetry group	H4, [3,3,5]
Properties	convex
Vertex figure Three truncated dodecahedrons and one tetrahedron meet at each vertex in an equilateral triangular pyramid arrangement.

In geometry, the truncated 120-cell is a uniform polychoron, constructed by a uniform truncation of the regular 120-cell polychoron.

It is made of 120 truncated dodecahedral and 600 tetrahedral cells. It has 3120 faces: 2400 being triangles and 720 being decagons. There are 4800 edges of two types: 3600 shared by three truncated dodecahedra and 1200 are shared by two truncated dodecahedra and one tetrahedron. Each vertex has 3 truncated dodecahedra and one tetrahedron around it. Its vertex figure is an equilateral triangular pyramid.

Contents 1 Images 2 See also 3 References 4 External links

[edit] Images

net	Central part of stereographic projection (centered on truncated tetrahedron)

[edit] See also

• Uniform polychoron

[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

[edit] External links

• Truncated hecatonicosachoron (36) from George Olshevsky's Convex uniform polychora
• Archimedisches Polychor Nr. 59 (stumpfer 120-Zeller) Marco Möller's Archimedean polytopes in R⁴ (German)
• Four-Dimensional Polytope Projection Barn Raisings (A Zometool construction of the truncated 120-cell), George W. Hart