Truncated 120-cells#Truncated 120-cell

File:Truncated hecatonicosachoron net.png]]

The truncated 120-cell or truncated hecatonicosachoron is a uniform 4-polytope, constructed by a uniform truncation of the regular 120-cell 4-polytope.

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.

• Truncated 120-cell (Norman W. Johnson)
• Tuncated hecatonicosachoron / Truncated dodecacontachoron / Truncated polydodecahedron
• Truncated-icosahedral hexacosihecatonicosachoron (Acronym thi) (George Olshevsky, and Jonathan Bowers)Klitizing, (o3o3x5x - thi)

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File:Hexacosihecatonicosachoron net.png]]

The bitruncated 120-cell or hexacosihecatonicosachoron is a uniform 4-polytope. It has 720 cells: 120 truncated icosahedra, and 600 truncated tetrahedra. Its vertex figure is a digonal disphenoid, with two truncated icosahedra and two truncated tetrahedra around it.

• Bitruncated 120-cell / Bitruncated 600-cell (Norman W. Johnson)
• Bitruncated hecatonicosachoron / Bitruncated hexacosichoron / Bitruncated polydodecahedron / Bitruncated polytetrahedron
• Truncated-icosahedral hexacosihecatonicosachoron (Acronym Xhi) (George Olshevsky, and Jonathan Bowers)Klitizing, (o3x3x5o - xhi)

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File:Truncated hexacosichoron net.png]]

The truncated 600-cell or truncated hexacosichoron is a uniform 4-polytope. It is derived from the 600-cell by truncation. It has 720 cells: 120 icosahedra and 600 truncated tetrahedra. Its vertex figure is a pentagonal pyramid, with one icosahedron on the base, and 5 truncated tetrahedra around the sides.

• Truncated 600-cell (Norman W. Johnson)
• Truncated hexacosichoron (Acronym tex) (George Olshevsky, and Jonathan Bowers)Klitizing, (x3x3o5o - tex)
• Truncated tetraplex (Conway)

The truncated 600-cell consists of 600 truncated tetrahedra and 120 icosahedra. The truncated tetrahedral cells are joined to each other via their hexagonal faces, and to the icosahedral cells via their triangular faces. Each icosahedron is surrounded by 20 truncated tetrahedra.

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• [http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471010030.html 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, {{isbn|978-0-471-01003-6}}
• (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
• [http://www.polytope.de Four-dimensional Archimedean Polytopes] (German), Marco Möller, 2004 PhD dissertation [http://www.sub.uni-hamburg.de/opus/volltexte/2004/2196/pdf/Dissertation.pdf] [http://www.polytope.de/nr58.html m58] [http://www.polytope.de/nr59.html m59] [http://www.polytope.de/nr53.html m53]
• {{PolyCell | urlname = section4.html| title = Convex uniform polychora based on the hecatonicosachoron (120-cell) and hexacosichoron (600-cell) - Model 36, 39, 41}}
• {{KlitzingPolytopes|polychora.htm|4D|uniform polytopes (polychora)}} o3o3x5x - thi, o3x3x5o - xhi, x3x3o5o - tex
• [http://www.georgehart.com/zome-polytopes-ISAMA07/hart-isama07.doc Four-Dimensional Polytope Projection Barn Raisings] (A Zometool construction of the truncated 120-cell), George W. Hart

• H4 uniform polytopes with coordinates: [http://eusebeia.dyndns.org/4d/trunc600cell t{3,3,5}] [http://eusebeia.dyndns.org/4d/trunc120cell t{5,3,3}] [http://eusebeia.dyndns.org/4d/bitrunc120cell 2t{5,3,3}]

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Category:Uniform 4-polytopes