The Pentagonal Bipyramid

The pentagonal bipyramid is a polyhedron bounded by 10 isosceles triangles, 15 edges, and 7 vertices. It is the dual of the pentagonal prism. It belongs to the class of duals of uniform polyhedra, which also includes the Catalan solids.

The pentagonal

The faces are transitive isosceles triangles with 2 short edges and 1 long edge. The edge length ratio is 3−φ : 2, or approximately 0.691 : 1, where φ=(1+√5)/2 is the Golden Ratio.

Note that the pentagonal bipyramid as the dual of the (uniform) pentagonal prism should not be confused with Johnson solid J13, which is also a pentagonal bipyramid, but with regular faces—equilateral triangles rather than isosceles triangles. The dual of J13 is a non-uniform pentagonal prism, having rectangular rather than square faces, with edge length ratio is √(25−11√5) : √2, or approximately 0.449 : 1.


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

Projection Description

Top view.

Edge-centered side view.

Oblique side view.

Face-centered view.


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

pentagonal bipyramid


The Cartesian coordinates for the pentagonal bipyramid are:

These coordinates correspond with a dual pentagonal prism of edge length (3φ−4).

Last updated 04 Dec 2023.

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