On rainbowness of semiregular polyhedra
- 30 Downloads
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.
Keywordsrainbowness Platonic solids prisms antiprisms Archimedean solids
Unable to display preview. Download preview PDF.
- V. G. Ashkinuze: On the number of semiregular polyhedra. Mat. Prosvesc. 1 (1957), 107–118. (In Russian.)Google Scholar
- H. S. M. Coxeter: Regular Potytopes. Dover Pub. New York, 1973.Google Scholar
- P. R. Cromwell: Polyhedra. Cambridge University Press, 1997.Google Scholar
- B. Grünbaum: Convex Polytopes (2nd edition). Springer Verlag, 2004.Google Scholar
- E. Jucovič: Convex Polyhedra. Veda, Bratislava, 1981. (In Slovak.)Google Scholar