We determine for which the complete graph has an embedding in whose topological symmetry group is isomorphic to one of the polyhedral groups , or .
Erica Flapan. Blake Mellor. Ramin Naimi. "Complete graphs whose topological symmetry groups are polyhedral." Algebr. Geom. Topol. 11 (3) 1405 - 1433, 2011. https://doi.org/10.2140/agt.2011.11.1405