The Elongated Pentagonal Orthocupolarotunda


The elongated pentagonal orthocupolarotunda is the 40th Johnson solid (J40). It has 35 vertices, 70 edges, and 37 faces (15 equilateral triangles, 15 squares, 7 pentagons).

The elongated pentagonal
orthocupolarotunda

The elongated pentagonal orthocupolarotunda 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 ortho­cupola­rotunda (J32). The ortho- in the name refers to how the top and bottom pentagons are aligned with each other. If they are rotated with respect to each other instead, the elongated penta­gonal gyrocupolarotunda (J41) is produced instead.

Projections

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

Projection Description

Top view.

Front view.

Side view.

Coordinates

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

where φ=(1+√5)/2 is the Golden Ratio.


Last updated 29 May 2018.

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