Geodesic
On rainbowness of semiregular polyhedra
Czechoslovak Mathematical Journal, Tome 58 (2008) no. 2, pp. 359-380

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MR Zbl
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.
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.
Classification : 05C15, 51M20, 52B05
Keywords: rainbowness; Platonic solids; prisms; antiprisms; Archimedean solids 
Jendroľ, Stanislav; Schrötter, Štefan. On rainbowness of semiregular polyhedra. Czechoslovak Mathematical Journal, Tome 58 (2008) no. 2, pp. 359-380. http://geodesic.mathdoc.fr/item/CMJ_2008_58_2_a4/
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