hexacontahedra

A hexacontahedron is a polyhedron with sixty faces. The term is a general one, and many different shapes can be classified as hexacontahedra. The specific arrangement and shape of these sixty faces determine the unique properties of each hexacontahedron. For instance, a hexacontahedron could be convex or concave, and its faces could be all identical or varied in shape and size.

One notable example is the deltoidal hexacontahedron, a Catalan solid. This particular hexacontahedron is the dual of the rhombic enneacontahedron, which is a near-miss Johnson solid. The faces of the deltoidal hexacontahedron are kites. Another significant type is the pentakis dodecahedron, which is also a hexacontahedron, but its faces are isosceles triangles. This shape arises from adding a pyramid to each face of a dodecahedron.

The study of hexacontahedra falls within the broader field of polyhedral geometry. Understanding their properties often involves analyzing their symmetry groups, vertex configurations, and the topological relationships between their faces, edges, and vertices. The diversity of forms a hexacontahedron can take makes it a rich area for geometric exploration.