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Four icosahedra can meet at a point

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Abstract

What is the maximal number of nonoverlapping copies of a regular polyhedron ∏ that can share a common vertex? The answer is shown to be 4 if ∏ is an icosahedron or dodecahedron, and is conjectured to be 7 for an octahedron and 20 for a tetrahedron. (For a cube the answer is trivially 8.)

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References

  1. Coxeter, H. S. M., Regular Polytopes (3rd edn), Dover, New York, 1973.

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Authors and Affiliations

  1. 15, rue des Acacias, F-69340, Francheville, France

    Henri Rossat

  2. Mathematical Sciences Research Center, At & T. Bell Laboratories, Room 2C-376, 07974, Murray Hill, NJ, U.S.A.

    N. J. A. Sloane

Authors
  1. Henri Rossat
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  2. N. J. A. Sloane
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Rossat, H., Sloane, N.J.A. Four icosahedra can meet at a point. Geom Dedicata 27, 219–222 (1988). https://doi.org/10.1007/BF00151354

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  • DOI: https://doi.org/10.1007/BF00151354

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