  A general (convex) polytope $P\subset\mathbb R^d$ and its edge-graph $G_P$
can have very distinct symmetry properties. We construct a coloring (of the
vertices and edges) of the edge-graph so that the combinatorial symmetry group
of the colored edge-graph is isomorphic (in a natural way) to
$\mathrm{Aut}_{\mathrm{GL}}(P)$, the group of linear symmetries of the
polytope. We also construct an analogous coloring for
$\mathrm{Aut}_{\mathrm{O}}(P)$, the group of orthogonal symmetries of $P$.
