disdyakis

The disdyakis is a type of dodecahedron, a polyhedron with twelve faces. Specifically, it is a topological polyhedron that can be formed by taking a dodecahedron and attaching a triangular pyramid to each of its twelve pentagonal faces. This process results in a polyhedron with a total of 24 triangular faces. Each vertex of the disdyakis has at least three faces meeting at it. The name "disdyakis" comes from the Greek words "di" meaning "two," "dyakis" meaning "triangular pyramid," and "hedra" meaning "face," referring to its structure of paired triangular pyramids on each original face.

This geometric shape can be visualized as a more complex version of a dodecahedron. When considering the arrangement of its faces and vertices, the disdyakis belongs to the class of polyhedra known as deltahedra, which are polyhedra whose faces are all equilateral triangles. However, not all disdyakis polyhedra are necessarily composed of equilateral triangles; the term can refer to topological equivalents where the faces are triangles but may not be equilateral. The disdyakis can be considered a specific example of a tetrakishexahedron or a trapezoidal dodecahedron in some contexts, depending on the precise geometric construction and symmetries.