Triangular tegum

''This article is about the general triangular bipyramid. For the Johnson solid J12, see triangular bipyramid (CRF). For the dual of the uniform triangular prism, see triangular bipyramid (uniform dual).''

The triangular bipyramid, also called a triangular dipyramid, is a bipyramid with a triangle as the equatorial section. Generally, a triangular bipyramid has 6 identical isosceles triangles as faces. It can be formed by joining two triangular pyramids at their bases.

Two specific cases of the general triangular bipyramid are notable. One such variation is obtained as the dual to the uniform triangular prism. The other is one of the Johnson solids, due to the pyramids being regular tetrahedra.

Notch
A notch is a variant of the triangular bipyramid constructed as the dual of a wedge. It has two isosceles triangles and four scalene triangles.

In vertex figures
The triangular bipyramid appears as the vertex figure of the nonuniform triangular duotegum. This vertex figure has an edge length of 1, and has no corealmic realization, because the Johnson triangular bipyramid has no circumscribed sphere. With an edge length of $\sqrt{2}$, it is also the vertex figure of the nonuniform square ditetragoltriate.

Variants of the triangular bipyramid (considered as a notch) by changing the edge opposite to a vertex appear as the vertex figure of the nonuniform ditetragoltriates. This vertex figure has an edge length of $\sqrt{2}$ for all other edges, and has no corealmic realization.