orientation preserving symmetries of a regular icosahedron . This is a $60$ element subgroup of $SO(3)$, isomorphic with the alternating group $A_5$. It is also perfect and self-normalizing in $SO(3)$. For each $g\in SO(3)$ the conjugate ${}^gI=gIg^{-1}$ is the group of rotations which leave invariant a rotated icosahedron. My question concerns