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

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  • Marek-Crnjac, L.

Abstract

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 Poincaré 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.

Suggested Citation

  • Marek-Crnjac, L., 2007. "Higher dimensional dodecahedra as models of the macro and micro universe in E-infinity Cantorian space-time," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 944-950.
    • Handle: RePEc:eee:chsofr:v:32:y:2007:i:3:p:944-950
    DOI: 10.1016/j.chaos.2006.07.030
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    1. El Naschie, M.S., 2006. "Elementary number theory in superstrings, loop quantum mechanics, twistors and E-infinity high energy physics," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 297-330.
    2. El Naschie, M.S., 2006. "Fuzzy Dodecahedron topology and E-infinity spacetime as a model for quantum physics," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1025-1033.
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    Cited by:

    1. Marek-Crnjac, L., 2009. "A short history of fractal-Cantorian space-time," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2697-2705.
    2. El Naschie, M.S., 2008. "High energy physics and the standard model from the exceptional Lie groups," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 1-17.
    3. He, Ji-Huan & Xu, Lan & Zhang, Li-Na & Wu, Xu-Hong, 2007. "Twenty-six dimensional polytope and high energy spacetime physics," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 5-13.
    4. Büyükkılıç, F. & Demirhan, D., 2009. "Cumulative growth with fibonacci approach, golden section and physics," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 24-32.
    5. Ješić, Siniša N., 2009. "Convex structure, normal structure and a fixed point theorem in intuitionistic fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 292-301.

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