Bipyramid

A bipyramid (also called a dipyramid) is a polyhedron formed by joining two congruent pyramids base-to-base. The common base is a polygon, and the two pyramids have apexes that lie on opposite sides of this base.

More formally, a bipyramid can be constructed by taking a pyramid with an n-sided polygonal base and gluing a second, congruent pyramid to the same base such that the resulting solid has 2n triangular faces, n + 2 vertices, and 3n edges.

Bipyramids are categorized based on the shape of their common polygonal base. For example, a triangular bipyramid has a triangular base, a square bipyramid has a square base, and so on. If the base is a regular polygon and the apexes are equidistant from the base, the bipyramid is a right regular bipyramid. If the pyramids are also regular tetrahedra, the triangular bipyramid is a Johnson solid (J12).

A special case of a bipyramid is the octahedron, which is a square bipyramid where all faces are equilateral triangles.