On rainbowness of semiregular polyhedra
Stanislav Jendroľ; Štefan Schrötter
Czechoslovak Mathematical Journal (2008)
- Volume: 58, Issue: 2, page 359-380
- ISSN: 0011-4642
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topJendroľ, Stanislav, and Schrötter, Štefan. "On rainbowness of semiregular polyhedra." Czechoslovak Mathematical Journal 58.2 (2008): 359-380. <http://eudml.org/doc/31215>.
@article{Jendroľ2008,
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.},
author = {Jendroľ, Stanislav, Schrötter, Štefan},
journal = {Czechoslovak Mathematical Journal},
keywords = {rainbowness; Platonic solids; prisms; antiprisms; Archimedean solids; rainbowness; Platonic solids; prisms; antiprisms; Archimedean solids},
language = {eng},
number = {2},
pages = {359-380},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On rainbowness of semiregular polyhedra},
url = {http://eudml.org/doc/31215},
volume = {58},
year = {2008},
}
TY - JOUR
AU - Jendroľ, Stanislav
AU - Schrötter, Štefan
TI - On rainbowness of semiregular polyhedra
JO - Czechoslovak Mathematical Journal
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 2
SP - 359
EP - 380
AB - 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.
LA - eng
KW - rainbowness; Platonic solids; prisms; antiprisms; Archimedean solids; rainbowness; Platonic solids; prisms; antiprisms; Archimedean solids
UR - http://eudml.org/doc/31215
ER -
References
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- Convex Polytopes (2nd edition), Springer Verlag, 2004. (2004) MR1976856
- Convex Polyhedra, Veda, Bratislava, 1981. (Slovak) (1981)
- 10.1016/j.disc.2005.01.010, Discrete Math. 303 (2005), 167–174. (2005) Zbl1084.05023MR2181051DOI10.1016/j.disc.2005.01.010
- Semi-regular polyhedra and maps, Geom. Dedicata 7 (1978), 465–478. (1978) Zbl0393.51009MR0512122
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