| Parabidiminished rhombicosidodecahedron | |
|---|---|
 | |
| Type | Canonical polyhedron, Johnson J79 – J80 – J81 |
| Faces | 10 triangles 2×10 squares 10 pentagons 2 decagons |
| Edges | 90 |
| Vertices | 50 |
| Vertex configuration | 20(4.5.10) 10+20(3.4.5.4) |
| Symmetry group | D5d |
| Dual polyhedron | - |
| Properties | convex |
| Net | |
 | |
In geometry, the parabidiminished rhombicosidodecahedron is one of the Johnson solids (J80). It is also a canonical polyhedron.
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A Johnson solid is one of 92 strictly convex polyhedra that are composed of regular polygon faces but are not uniform polyhedra (that is, they are not Platonic solids , Archimedean solids , prisms , or antiprisms ). They were named by Norman Johnson , who first listed these polyhedra in 1966. [1]
It can be constructed as a rhombicosidodecahedron with two opposing pentagonal cupolae removed. Related Johnson solids are the diminished rhombicosidodecahedron (J76) where one cupola is removed, the metabidiminished rhombicosidodecahedron (J81) where two non-opposing cupolae are removed, and the tridiminished rhombicosidodecahedron (J83) where three cupolae are removed.
