A planar triangulation is a planar drawing of a maximal planar graph such that any two edges intersect at most at their endpoints and each face is bounded by a cycle of length three contained in the planar graph. In this paper, we investigate the construction of polyhedra arising from maximal planar graphs. In particular, we construct a family of maximal planar graphs with dihedral automorphism groups. Moreover, we demonstrate that these graphs can be realized as polyhedra with congruent triangular faces in the Euclidean 3-space having dihedral symmetry groups. We achieve this result by exploiting Grünbaum-colorings.