The Triangular Bipyramid

The triangular bipyramid is a polyhedron bounded by 6 isosceles triangles, 9 edges, and 5 vertices. It is the dual of the triangular prism. It belongs to the class of duals of uniform polyhedra, which also includes the Catalan solids.

The triangular

The faces are transitive isosceles triangles with 2 short edges and 1 long edge. The edge length ratio is 2 : 3.

Note that the triangular bipyramid as the dual of the (uniform) triangular prism should not be confused with Johnson solid J12, which is also a triangular bipyramid, but with regular faces—equilateral triangles—rather than isosceles triangles. The dual of J12 is a non-uniform triangular prism, having rectangular faces with edge ratio √6 : 1 rather than squares.


The following are images of the triangular bipyramid from various viewpoints:

Projection Description

Top view.

Front view, looking at an equatorial vertex.

Face-centered view.

Oblique side view.


Here's an animation of the triangular bipyramid rotating around its vertical axis:

triangular bipyramid


The Cartesian coordinates for the triangular bipyramid are:


The triangular bipyramid occurs as cells in the joined pentachoron, the dual of the rectified 5-cell, one of the 4D Catalan polychora.

Last updated 12 Jul 2023.

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