hexoctahedral

The term "hexoctahedral" refers to a geometric concept often encountered in crystallography and polyhedral geometry. It describes a specific type of polyhedron or a crystal system. In crystallography, the hexoctahedral class is one of the 32 crystal classes and belongs to the cubic crystal system. It is characterized by its high degree of symmetry, possessing the highest symmetry possible within the cubic system.

A hexoctahedron, as a polyhedron, can be thought of as a complex form derived from the octahedron. It has 48 faces, 72 edges, and 26 vertices. These faces are typically scalene triangles, meaning they have sides of different lengths. The symmetry elements of the hexoctahedral class include a center of inversion, four threefold rotation axes, three fourfold rotation axes, and six twofold rotation axes. This extensive symmetry gives rise to its name, suggesting a combination of octahedral and possibly other related symmetries.

In the context of mineralogy, minerals exhibiting the hexoctahedral crystal habit are rare but may include certain metallic elements or compounds that crystallize under specific conditions favoring high symmetry. The precise geometric description and the number of faces can vary depending on the specific interpretation or classification system being used, but the core concept revolves around a highly symmetrical structure with numerous triangular faces.