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.

Projections

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

Projection	Description
	Top view.
	Front view.
	Side view.

Coordinates

The Cartesian coordinates of the parabidiminished rhombicosidodecahedron with edge length 2 are:

• (±1, ±1, ±φ³)
• (±1, ±φ³, ±1)
• (φ³, ±1, −1)
• (−φ³, ±1, 1)

• (±φ, ±φ², ±2φ)
• (±φ², ±2φ, ±φ)
• (2φ, ±φ, −φ²)
• (−2φ, ±φ, φ²)

• (0, ±(φ+2), ±φ²)
• (±(φ+2), ±φ², 0)
• (φ², 0, −(φ+2))
• (−φ², 0, (φ+2))

where φ=(1+√5)/2 is the Golden Ratio.