Geometric realizations of regular abstract polyhedra with automorphism group $H_3$

Jonn Angel L. Aranas, Mark L. Loyola

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…