The Parabidiminished Rhombicosidodecahedron

The parabidiminished rhombicosidodecahedron is the 80th Johnson solid, or J80 for short. It has 42 faces (2 decagons, 10 pentagons, 20 squares, and 10 triangles), 90 edges, and 42 vertices. It is obtained by cutting off two pentagonal cupolae segment from opposite sides of the rhombicosidodecahedron.

A parabidiminished


Here are some views of the parabidiminished rhombicosidodecahedron from various angles:

Projection Description

Top view.

Front view.

Side view.


The Cartesian coordinates of the parabidiminished rhombicosidodecahedron with edge length 2 are even permutations of coordinate and all changes of sign of:

where φ=(1+√5)/2 is the Golden Ratio.

Last updated 18 Mar 2019.

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