Czechoslovak Mathematical Journal

, Volume 58, Issue 2, pp 359–380 | Cite as

On rainbowness of semiregular polyhedra

  • Stanislav Jendroľ
  • Štefan Schrötter


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.


rainbowness Platonic solids prisms antiprisms Archimedean solids 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    V. G. Ashkinuze: On the number of semiregular polyhedra. Mat. Prosvesc. 1 (1957), 107–118. (In Russian.)Google Scholar
  2. [2]
    H. S. M. Coxeter: Regular Potytopes. Dover Pub. New York, 1973.Google Scholar
  3. [3]
    P. R. Cromwell: Polyhedra. Cambridge University Press, 1997.Google Scholar
  4. [4]
    L. Fejes Tóth: Regular Figures. Pergamon Press, Oxford, 1964.MATHGoogle Scholar
  5. [5]
    B. Grünbaum: Convex Polytopes (2nd edition). Springer Verlag, 2004.Google Scholar
  6. [6]
    E. Jucovič: Convex Polyhedra. Veda, Bratislava, 1981. (In Slovak.)Google Scholar
  7. [7]
    S. Negami: Looseness ranges of triangulations on closed surfaces. Discrete Math. 303 (2005), 167–174.CrossRefMathSciNetMATHGoogle Scholar
  8. [8]
    J. Zaks: Semi-regular polyhedra and maps. Geom. Dedicata 7 (1978), 465–478.CrossRefMathSciNetMATHGoogle Scholar

Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2008

Authors and Affiliations

  1. 1.Institute of MathematicsP. J. Šafárik UniversityKošiceSlovak Republic
  2. 2.Department of MathematicsTechnical UniversityKošiceSlovak Republic

Personalised recommendations