Bipüramidaalset

Bipüramidaalset, also known as a dipyramid or bipyramid, is a polyhedron composed of two identical pyramids joined at their bases. The resulting shape is symmetrical along the plane of the shared base. The number of faces on a bipüramidaalset is equal to twice the number of sides of the base polygon of the pyramids. For instance, a triangular bipüramidaalset (formed from two triangular pyramids) has six faces, while a square bipüramidaalset has eight faces.

The vertices of a bipüramidaalset include the apexes of the two pyramids and the vertices of the common base. The edges consist of the edges of the common base and the lateral edges connecting the base vertices to the respective apexes. Bipüramidaalsets can be convex or non-convex, depending on the shape of the pyramids and their base.

Common examples of bipüramidaalsets include the triangular bipüramidaalset, square bipüramidaalset, and pentagonal bipüramidaalset. These shapes appear in various contexts, including crystallography, where certain crystal habits can resemble bipüramidaalsets. They are also studied in geometry for their properties related to symmetry and volume calculation. The concept can be generalized to n-dimensional spaces, where an n-dimensional bipüramidaalset is formed by joining two n-dimensional pyramids at their (n-1)-dimensional bases.