bipüramidaalsets

Bipüramidaalsets, also known as a dipyramid or bipyramid, is a polyhedron formed by joining two pyramids base-to-base. The two pyramids share a common base, which is a polygon. The resulting shape has two apexes, one on each side of the common base, and the faces are all triangles. The number of faces, edges, and vertices of a bipüramidaalsets depends on the number of sides of the polygonal base. For example, a triangular bipüramidaalsets has a triangular base, resulting in six triangular faces, nine edges, and five vertices. A square bipüramidaalsets has a square base and eight triangular faces, twelve edges, and six vertices.

Bipüramidaalsets can be classified as either regular or irregular. A regular bipüramidaalsets has a regular polygon as its base and all its triangular faces are congruent isosceles triangles. The Johnson solids include several examples of regular bipüramidaalsets, such as the triangular, square, and pentagonal bipüramidaalsets. Irregular bipüramidaalsets can have any polygon as their base and their triangular faces may not be congruent or isosceles.

In crystallography, bipüramidaalsets are a common crystal habit, particularly for minerals that crystallize in the ditrigonal or hexagonal systems. The dipyramidal form is characterized by the presence of two pyramids joined at their bases, creating a shape that is elongated along a central axis. Examples of minerals that often exhibit a dipyramidal habit include quartz, rutile, and zircon. This geometric form is a consequence of the specific arrangement of atoms within the crystal lattice.