Triangular Prism. In geometry, a right triangular prism is a three-sided prism. A polyhedron with two congruent and parallel faces and whose lateral faces are parallelograms. The shape of the base gives the prism its name.That is, a prism with triangular bases is a triangular prism.riangular Prism. In geometry, a right triangular prism is a three-sided prism. A polyhedron with two congruent and parallel faces and whose lateral faces are parallelograms. The shape of the base gives the prism its name.