A triangular bipyramid is a hexahedron, a polyhedron with six triangular faces. It is constructed by attaching two tetrahedra face-to-face. The same shape is also known as a triangular dipyramid or trigonal bipyramid. If these tetrahedra are regular, all faces of a triangular bipyramid are equilateral. It is an example of a deltahedron, composite polyhedron, and Johnson solid.

Many polyhedra are related to the triangular bipyramid, such as similar shapes derived from different approaches and the triangular prism as its dual polyhedron. Applications of a triangular bipyramid include trigonal bipyramidal molecular geometry, which describes its atom cluster, a solution of the Thomson problem, and the representation of color order systems by the eighteenth century.

Like other bipyramids, a triangular bipyramid can be constructed by attaching two tetrahedra face-to-face. These tetrahedra cover their triangular base, and the resulting polyhedron has six triangles, five vertices, and nine edges. Because of its triangular faces with any type, the triangular bipyramid is a simplicial polyhedron like other infinitely many bipyramids. A right bipyramid is one in which the apices of both pyramids are on a line passing through the center of the base, such that its faces are isosceles triangles. If two tetrahedra are otherwise, the triangular bipyramid is oblique.

According to Steinitz's theorem, a graph can be represented as the skeleton of a polyhedron if it is a planar (can be drawn without crossing any edges) and three-connected graph (it remains connected if any two vertices are removed). A triangular bipyramid is represented by a graph with nine edges, constructed by adding one vertex to the vertices of a wheel graph representing tetrahedra.

Like other right bipyramids, a triangular bipyramid has three-dimensional point-group symmetry, the dihedral group ${\displaystyle D_{3\mathrm {h} }}$ of order twelve: the appearance of a triangular bipyramid is unchanged as it rotated by one-, two-thirds, and full angle around the axis of symmetry (a line passing through two vertices and the base's center vertically), and it has mirror symmetry with any bisector of the base; it is also symmetrical by reflection across a horizontal plane. A triangular bipyramid is face-transitive (or isohedral).

If the tetrahedra are regular, all edges of a triangular bipyramid are equal in length and form equilateral triangular faces. A polyhedron with only equilateral triangles as faces is called a deltahedron. There are eight convex deltahedra, one of which is a triangular bipyramid with regular polygonal faces. A convex polyhedron in which all of its faces are regular polygons is a Johnson solid. A triangular bipyramid with regular faces is numbered as the twelfth Johnson solid ${\displaystyle J_{12}}$. It is an example of a composite polyhedron because it is constructed by attaching two regular tetrahedra.

A triangular bipyramid's surface area ${\displaystyle A}$ is six times that of each triangle. Its volume ${\displaystyle V}$ can be calculated by slicing it into two tetrahedra and adding their volume. In the case of edge length ${\displaystyle a}$, this is: $${\displaystyle {\begin{aligned}A&={\frac {3{\sqrt {3}}}{2}}a^{2}&\approx 2.598a^{2},\\V&={\frac {\sqrt {2}}{6}}a^{3}&\approx 0.238a^{3}.\end{aligned}}}$$

The dihedral angle of a triangular bipyramid can be obtained by adding the dihedral angle of two regular tetrahedra. The dihedral angle of a triangular bipyramid between adjacent triangular faces is that of the regular tetrahedron: 70.5 degrees. In an edge where two tetrahedra are attached, the dihedral angle of adjacent triangles is twice that: 141.1 degrees.