| Title:
|
On rainbowness of semiregular polyhedra (English) |
| Author:
|
Jendroľ, Stanislav |
| Author:
|
Schrötter, Štefan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
58 |
| Issue:
|
2 |
| Year:
|
2008 |
| Pages:
|
359-380 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
rainbowness |
| Keyword:
|
Platonic solids |
| Keyword:
|
prisms |
| Keyword:
|
antiprisms |
| Keyword:
|
Archimedean solids |
| MSC:
|
05C15 |
| MSC:
|
51M20 |
| MSC:
|
52B05 |
| idZBL:
|
Zbl 1174.51010 |
| idMR:
|
MR2411095 |
| . |
| Date available:
|
2009-09-24T11:55:21Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128263 |
| . |
| Reference:
|
[1] V. G. Ashkinuze: On the number of semiregular polyhedra.Mat. Prosvesc. 1 (1957), 107–118. (Russian) |
| Reference:
|
[2] H. S. M. Coxeter: Regular Potytopes.Dover Pub. New York, 1973. MR 0370327 |
| Reference:
|
[3] P. R. Cromwell: Polyhedra.Cambridge University Press, 1997. Zbl 0888.52012, MR 1458063 |
| Reference:
|
[4] L. Fejes Tóth: Regular Figures.Pergamon Press, Oxford, 1964. MR 0165423 |
| Reference:
|
[5] B. Grünbaum: Convex Polytopes (2nd edition).Springer Verlag, 2004. MR 1976856 |
| Reference:
|
[6] E. Jucovič: Convex Polyhedra.Veda, Bratislava, 1981. (Slovak) |
| Reference:
|
[7] S. Negami: Looseness ranges of triangulations on closed surfaces.Discrete Math. 303 (2005), 167–174. Zbl 1084.05023, MR 2181051, 10.1016/j.disc.2005.01.010 |
| Reference:
|
[8] J. Zaks: Semi-regular polyhedra and maps.Geom. Dedicata 7 (1978), 465–478. Zbl 0393.51009, MR 0512122 |
| . |
