The Elongated Pentagonal Gyrocupolarotunda

The elongated pentagonal gyrocupolarotunda is the 41st Johnson solid (J41). It has 35 vertices, 70 edges, and 37 faces (15 equilateral triangles, 15 squares, 7 pentagons).

The elongated pentagonal

The elongated pentagonal gyrocupolarotunda can be constructed by attaching a pentagonal rotunda and a pentagonal cupola to a decagonal prism. Or equivalently, inserting a decagonal prism between the rotunda and cupola parts of a pentagonal gyro­cupola­rotunda (J33). 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 ortho­cupola­rotunda (J40) is produced instead.


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

Projection Description

Top view.

Front view.

Side view.


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

where φ=(1+√5)/2 is the Golden Ratio.

Last updated 17 May 2018.

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