The Pentagonal Bipyramid

The pentagonal bipyramid is the 13th Johnson solid (J13). It has 7 vertices, 15 edges, and 10 faces (10 equilateral triangles).

The pentagonal

The pentagonal bipyramid can be constructed by attaching two pentagonal pyramids to each other at their bases.

The dual of J13 is a non-uniform pentagonal prism, with longer edges along its axis of symmetry than the edges in the pentagonal caps. The edge length ratio is √(25−11√5) : √2, or approximately 0.449 : 1. Thus, J13 is not to be confused with the dual of a uniform pentagonal prism, also a pentagonal bipyramid but with isosceles triangles rather than equilateral triangles as faces.


Here are some views of the pentagonal bipyramid from various angles:

Projection Envelope Description
Regular pentagon

Top view.


Side view.


Front view.


The Cartesian coordinates of the pentagonal bipyramid with edge length 2 are:

where φ=(1+√5)/2 is the Golden Ratio.


The pentagonal bipyramid occurs as cells in some CRF polychora, including (but not limited to):

Last updated 11 Aug 2023.

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