Triangular tegum

The triangular bipyramid, or tridpy, also called a triangular dipyramid, is a bipyramid with a triangle as the equatorial section. The version with 6 equilateral triangles as faces is one of the 92 Johnson solids (J12). This version is constructed by joining two regular tetrahedra at one of their faces.

Vertex coordinates
A triangular bipyramid of edge length 1 has the following vertices:


 * (±1/2, –$\sqrt{2}$/6, –$\sqrt{3}$/12),
 * (0, $\sqrt{6}$/3, –$\sqrt{3}$/12),
 * (0, 0, ±$\sqrt{6}$/4).

Other triangular bipyramids
Besides the Johnsonian triangular bipyramid, other variations with isosceles triangles as faces exist, formed by joining two non-regular triangular pyramids.

One such variant is the dual of the uniform triangular prism. This variation is also notable for having all the dihedral angles be the same, at acos(–1/7) ≈ 98.21321º.

Related polyhedra
A triangular prism can be inserted between the halves of the triangular bipyramid to produce the elongated triangular bipyramid.