Higher dimensional dodecahedra as models of the macro and micro universe in E-infinity Cantorian space-time

In this short work, we present a summary about Platonic solids specially about the different dodecahedra. Kepler's Conjecture and the Dodecahedral Conjecture are of a great importance in circle searching specially in the Poincare dodecahedron space as a cosmological model. Some properties of the 120-cell Coxeter polytop are presented. E-infinity Cantorian space-time may be regarded as a fuzzy version of a hyperbolic manifold based on the 120-cell Coxeter polytop. The topology of fuzzy 4-dimensional polytops are used to give information about the number of the elementary particles in the standard model of high energy physics. (c) 2006 Elsevier Ltd. All rights reserved.