triaconthedra

A triacontadron is a polyhedron with 30 faces. The term is derived from Greek words: "triaconta" meaning thirty and "hedra" meaning face. There are many different types of triacontadra, as the shape and arrangement of the 30 faces can vary widely. Some triacontadra are convex, while others are non-convex or even self-intersecting.

One notable example of a triacontadron is the rhombic triacontadron, a convex polyhedron with 30 identical rhombus-shaped faces. This shape is the dual of the icosidodecahedron. Another example is the deltoidal hexecontahedron, which is also a convex polyhedron with 30 faces, but these faces are kite-shaped. The specific geometric properties, such as the number of vertices and edges, depend on the precise arrangement and type of faces.

Triacontadra can arise in various contexts, including crystallography, where mineral structures can exhibit these faces. In mathematics, they can be explored as part of the study of polyhedra and their topological properties. The concept of a triacontadron is broad, encompassing any solid figure bounded by thirty planar surfaces. Further classification and study often focus on specific types of triacontadra based on the regularity and symmetry of their faces and vertices.