We show that the topological symmetry group of a canonically embedded complete graph of $n\geq 7$ vertices in the 3-sphere is isomorphic to a dihedral group of order $2n$.
"The Topological Symmetry Group of a Canonically Embedded Complete Graph in $S^3$." Tokyo J. Math. 20 (1) 45 - 50, June 1997. https://doi.org/10.3836/tjm/1270042397