We prove that Platonic and some Archimedean polyhedra have the fixed point property in a non-classical sense.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba61-3-8, author = {Dariusz Miklaszewski}, title = {Fixed Points of Maps of Sets of Polyhedra into the Disc}, journal = {Bulletin of the Polish Academy of Sciences. Mathematics}, volume = {61}, year = {2013}, pages = {263-275}, zbl = {1293.55002}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba61-3-8} }
Dariusz Miklaszewski. Fixed Points of Maps of Sets of Polyhedra into the Disc. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 61 (2013) pp. 263-275. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba61-3-8/