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Diminished rhombicosidodecahedron 
Summary
In geometry, the diminished rhombicosidodecahedron is one of the Johnson solids (J76). It can be constructed as a rhombicosidodecahedron with one pentagonal cupola removed.
| Diminished rhombicosidodecahedron | |
|---|---|
 | |
| Type | Johnson J75 – J76 – J77 |
| Faces | 3x5 triangles 3x5+10 squares 1+2x5 pentagons 1 decagon |
| Edges | 105 |
| Vertices | 55 |
| Vertex configuration | 10(4.5.10) 3x5+3x10(3.4.5.4) |
| Symmetry group | C5v |
| Dual polyhedron | - |
| Properties | convex |
| Net | |
 | |
A Johnson solid is one of 92 strictly convex polyhedra that is 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.
External links edit
- Weisstein, Eric W., "Diminished rhombicosidodecahedron" ("Johnson solid") at MathWorld.
- Editable printable net of a diminished rhombicosidodecahedron with interactive 3D view
- ^ Johnson, Norman W. (1966), "Convex polyhedra with regular faces", Canadian Journal of Mathematics, 18: 169–200, doi:10.4153/cjm-1966-021-8, MR 0185507, Zbl 0132.14603.