Editing Triangular bipyramid (section)

== Related polyhedra ==
[[File:GoldnerHararyJmol2C.jpg|alt=Geometric realization of the Goldner–Harary graph|The Goldner–Harary graph represents a triangular bipyramid, augmented by tetrahedra.|thumb|upright]]
Some types of triangular bipyramids may be derived in different ways. The [[Kleetope]] of a polyhedron is a construction involving the attachment of pyramids. A triangular bipyramid's Kleetope can be constructed from a triangular bipyramid by attaching tetrahedra to each of its faces, replacing them with three other triangles; the skeleton of the resulting polyhedron represents the [[Goldner–Harary graph]].{{r|grunbaum|ewald}} Another type of triangular bipyramid results from cutting off its vertices, a process known as [[Truncation (geometry)|truncation]].{{r|hceg}}

Bipyramids are the [[dual polyhedron]] of [[Prism (geometry)|prisms]]. This means the bipyramids' vertices correspond to the faces of a prism, and the edges between pairs of vertices of one correspond to the edges between pairs of faces of the other; doubling it results in the original polyhedron. A triangular bipyramid is the dual polyhedron of a [[triangular prism]], and vice versa.{{r|sibley|king}} A triangular prism has five faces, nine edges, and six vertices, with the same symmetry as a triangular bipyramid.{{r|king}}