| Diminished rhombicosidodecahedron | |
|---|---|
 | |
| Type | Johnson J75 – J76 – J77 |
| Faces | 3×5 triangles 3×5+10 squares 1+2×5 pentagons 1 decagon |
| Edges | 105 |
| Vertices | 55 |
| Vertex configuration | 10(4.5.10) 3×5+3×10(3.4.5.4) |
| Symmetry group | C5v |
| Dual polyhedron | - |
| Properties | convex |
| Net | |
 | |
In geometry, the diminished rhombicosidodecahedron is one of the Johnson solids (J76). It can be constructed as a rhombicosidodecahedron with one pentagonal cupola removed.
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]
Related Johnson solids are:
- J80: parabidiminished rhombicosidodecahedron with two opposing cupolae removed, and
- J81: metabidiminished rhombicosidodecahedron with two non-opposing cupolae removed, and
- J83: tridiminished rhombicosidodecahedron with three cupola removed.