Trapezohedrons

A trapezohedron is a polyhedron that is the dual of a gyrobifastigium. It is a type of kite polyhedron, meaning all its faces are congruent kites. Specifically, a trapezohedron has 2n faces, where n is an integer greater than or equal to 3. The faces are arranged in pairs, with each pair forming a kite shape. These kites are not necessarily rhombuses. The trapezohedron has 2n vertices and 4n edges.

The simplest trapezohedron is the trigonal trapezohedron, which has 6 faces, 12 edges, and 8 vertices. It is also known as the trigonal deltohedron. The next is the tetragonal trapezohedron with 8 faces, 16 edges, and 10 vertices, and the pentagonal trapezohedron with 10 faces, 20 edges, and 12 vertices.

Trapezohedrons are also called deltohedrons or kite polyhedra. They are related to the Catalan solids, which are the duals of the Archimedean solids. However, trapezohedrons are not themselves Catalan solids, as their faces are not necessarily regular polygons. In crystallography, trapezohedrons appear as forms, such as the trapezohedral form of garnet.