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On rainbowness of semiregular polyhedra

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Abstract

We introduce the rainbowness of a polyhedron as the minimum number k such that any colouring of vertices of the polyhedron using at least k colours involves a face all vertices of which have different colours. We determine the rainbowness of Platonic solids, prisms, antiprisms and ten Archimedean solids. For the remaining three Archimedean solids this parameter is estimated.

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Authors and Affiliations

  1. Institute of Mathematics, P. J. Šafárik University, Jesenná 5, SK-041 54, Košice, Slovak Republic

    Stanislav Jendroľ

  2. Department of Mathematics, Technical University, Letná 9, SK-042 00, Košice, Slovak Republic

    Štefan Schrötter

Authors
  1. Stanislav Jendroľ
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  2. Štefan Schrötter
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Corresponding author

Correspondence to Stanislav Jendroľ.

Additional information

Dedicated to Professor Miroslav Fiedler on the occasion of his 80th birthday.

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Jendroľ, S., Schrötter, Š. On rainbowness of semiregular polyhedra. Czech Math J 58, 359–380 (2008). https://doi.org/10.1007/s10587-008-0021-z

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  • DOI: https://doi.org/10.1007/s10587-008-0021-z

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