The Triangular Bipyramid
The triangular bipyramid is the 12th Johnson solid (J12). It has 5 vertices, 9 edges, and 6 faces (6 equilateral triangles).
The triangular bipyramid can be constructed by attaching two tetrahedra to each other.
If a triangular prism is inserted between the two constituent tetrahedra, an elongated triangular bipyramid (J14) is produced.
The triangular pyramid (J12) is the dual of a non-uniform triangular prism, one with rectangular faces with edge ratio √6 : 1 rather than squares. The dual of the uniform triangular prism is a different triangular pyramid—one with isosceles triangles (with edge ratio 2 : 3) rather than equilateral triangles.
Projections
Here are some views of the triangular bipyramid from various angles:
| Projection | Envelope | Description |
|---|---|---|
 |
Triangle | Top view. |
 |
Tetragon | Side view. |
 |
Rhombus | Front view. |
Coordinates
The Cartesian coordinates of the triangular bipyramid with edge length 2 are:
- (±1, −1/√3, 0)
- (0, 2/√3, 0)
- (0, 0, ±√(8/3))
