| Metagyrate diminished rhombicosidodecahedron | |
|---|---|
 | |
| Type | Johnson J77 – J78 – J79 |
| Faces | 3+6×2 triangles 3+11×2 squares 3+4×2 pentagons 1 decagon |
| Edges | 105 |
| Vertices | 55 |
| Vertex configuration | 5×2(4.5.10) 5×2(3.42.5) 3+16×2(3.4.5.4) |
| Symmetry group | Cs |
| Dual polyhedron | - |
| Properties | convex |
| Net | |
 | |
In geometry, the metagyrate diminished rhombicosidodecahedron is one of the Johnson solids (J78). It can be constructed as a rhombicosidodecahedron with one pentagonal cupola (J5) rotated through 36 degrees, and a non-opposing pentagonal cupola removed. (The cupolae cannot be adjacent.)
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]