There are five platonic solids, and 13/15 (which is correct?) Archimedean Solids. The finite groups of isometries of Euclidean $3$-space are the finite subgroups of $SO(3,\mathbb{R})$ or $O(3,\mathbb{R})=SO(3,\mathbb{R})\times \mathbb{Z}_2$.
Question: List all the finite subgroups of $O(3,\mathbb{R})$. Further, which groups are the full group of symmetries of Archimedean solids.
[I am familiar with finite subgroups of $SO(3,\mathbb{R})$, which are symmetry groups of platonic solids. I want to consider finite subgroups of $O(3,\mathbb{R})$ and their connection with Archimedean solids.]