The Elongated Pentagonal Gyrobicupola

The elongated pentagonal gyrobicupola is the 39th Johnson solid (J39). It has 30 vertices, 60 edges, and 32 faces (10 equilateral triangles, 20 squares, 2 pentagons).

The elongated pentagonal

The elongated pentagonal gyrobicupola can be constructed by attaching two pentagonal cupolae to a decagonal prism, or equivalently, inserting a decagonal prism between the two halves of the pentagonal gyrobicupola (J31). The gyro- in the name refers to how the top and bottom pentagons are rotated with respect to each other. If they are aligned with each other instead, the elongated pentagonal ortho­bicupola (J38) is produced instead.


Here are some views of the elongated pentagonal gyrobicupola from various angles:

Projection Description

Top view.

Front view.

Side view.


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

where φ=(1+√5)/2 is the Golden Ratio.

Last updated 29 May 2018.

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