I’m curious about the finite subgroups of $\mathrm{GL}_3(\mathbb{R})$. I’ve looked around, but have only been able to find a classification of the finite subgroups in
- $\mathrm{SL}_2(\mathbb{C})$ and $\mathrm{SL}_3(\mathbb{C})$;
- $\mathrm{SO}(3,\mathbb{R})$;
- and $\mathrm{GL}_3(\mathbb{Z})$ ...
... but not all of $\mathrm{GL}_3(\mathbb{R})$. Is there a complete classification of the finite subgroups in this setting (up to isomorphism)? If so, what is it?
Just for fun context, the reason I ask is because I’m curious about the construction detailed here regarding building a polytope from a faithful group representation. It seems like it would be neat to actually see all the polyhedra you can get in $\mathbb{R}^3$.