120-cell is one of 15 regular and uniform polytopes with the same H4 symmetry [3,3,5]: {p,3,3} polytopes The 120-cell is similar to three regular 4-polytopes: the 5-cell {3,3,3} and tesseract {4,3,3} of Euclidean 4-space, and the hexagonal tiling honeycomb {6,3,3} of hyperbolic space. All of these have a tetrahedral vertex figure {3,3}: {5,3,p} polytopes The 120-cell is a part of a sequence of 4-polytopes and honeycombs with dodecahedral cells: Davis 120-cell The Davis 120-cell, introduced by , is a compact 4-dimensional hyperbolic manifold obtained by identifying opposite faces of the 120-cell, whose universal cover gives the regular honeycomb {5,3,3,5} of 4-dimensional hyperbolic space. See also Uniform 4-polytope family with [5,3,3] symmetry 57-cell – an abstract regular 4-polytope constructed from 57 hemi-dodecahedra. 600-cell - the dual 4-polytope to the 120-cell Notes Citations References (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 Four-dimensional Archimedean Polytopes (German), Marco Möller, 2004 PhD dissertation External links Der 120-Zeller (120-cell) Marco Möller's Regular polytopes in R4 (German) 120-cell explorer – A free interactive program that allows you to learn about a number of the 120-cell symmetries. The 120-cell is projected to 3 dimensions and then rendered using OpenGL. Construction of the Hyper-Dodecahedron YouTube animation of the construction of the 120-cell Gian Marco Todesco. Individual graphs 120 Articles containing video clips