Pyritohedras

Pyritohedras are a class of polyhedra that exhibit pentagonal symmetry. They are characterized by faces that are irregular pentagons, and they possess the same rotational symmetry as a pentagonal antiprism. The name "pyritohedra" is derived from pyrite, a mineral that commonly crystallizes in a form resembling this shape. Specifically, pyrite often forms twinned crystals where two interpenetrating pyritohedra meet at a common face. While natural pyritohedra are often distorted, the ideal geometric form is a key concept in crystallography and solid-state physics. These polyhedra can be described mathematically as having 12 faces, 20 vertices, and 30 edges. Each vertex is shared by three faces. The angles between the faces and the lengths of the edges are not all equal, contributing to their irregular appearance. The study of pyritohedra is important for understanding the morphology and internal structure of crystalline materials.