Complete graphs whose topological symmetry groups are polyhedral
classification
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keywords
completegroupspolyhedralsymmetrytopologicalwhosedetermineembedding
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We determine for which $m$, the complete graph $K_m$ has an embedding in $S^3$ whose topological symmetry group is isomorphic to one of the polyhedral groups: $A_4$, $A_5$, or $S_4$.
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