  A \textit{geometric realization} of an abstract polyhedron $\mathcal{P}$ is a
mapping $\rho : \mathcal{P} \to \mathbb{E}^3$ that sends an $i$-face to an open
set of dimension $i$. This work adapts a method based on Wythoff construction
to generate a full rank realization of a regular abstract polyhedron from its
automorphism group $\Gamma$. The method entails finding a real orthogonal
representation of $\Gamma$ of degree 3 and applying its image to suitably
chosen open sets in space. To demonstrate the use of the method, we apply it to
the abstract polyhedra whose automorphism groups are isomorphic to the
non-crystallographic Coxeter group $H_3$.
