pyritohedral

Pyritohedral is an adjective used in geometry and crystallography to describe things related to pyritohedral symmetry, a form of symmetry named after the crystal habit of pyrite. It denotes shapes or arrangements that exhibit a specific, comparatively high degree of symmetry associated with pyrite-like crystals.

In geometry, pyritohedral symmetry describes a class of polyhedra that share a distinctive set of symmetry operations. Shapes with pyritohedral symmetry are not fully icosahedral, but they exhibit regularities that resemble the way pyrite crystals grow. A notable example is the pyritohedron, a convex polyhedron with twelve pentagonal faces that reflects the hallmark features of this symmetry. The faces are not regular pentagons in general, but they are arranged so the overall figure respects the pyritohedral group of symmetries. The pyritohedron and related forms are often discussed in the context of Catalan solids and duals of Archimedean solids, highlighting the connection between face structure and symmetry.

In crystallography, pyritohedral symmetry is a crystallographic point group used to classify certain mineral forms and crystal habits. It provides a symmetry framework that sits between the more common tetrahedral, octahedral, and icosahedral classes, capturing the characteristic distribution of axes and mirror planes observed in some pyrite-like crystals.

Variants or families of shapes described as pyritohedral can be generated by applying the same symmetry constraints to different base forms, yielding a range of polyhedra with twelve pentagonal faces and the defining pyritohedral symmetry. The term is primarily of interest in theoretical geometry and mineralogy, where symmetry considerations guide classification and modeling. See also pyrite, pyritohedron, symmetry, and Catalan solids.