Gyrate bidiminished rhombicosidodecahedron
82nd Johnson solid
| Gyrate bidiminished rhombicosidodecahedron | |
|---|---|
 | |
| Type | Johnson J81 – J82 – J83 |
| Faces | 10 triangles 20 squares 10 pentagons 2 decagons |
| Edges | 90 |
| Vertices | 50 |
| Vertex configuration | 10.2(4.5.10) 5x2(3.42.5) 4+8.2(3.4.5.4) |
| Symmetry group | Cs |
| Dual polyhedron | - |
| Properties | Convex |
| Net | |
 | |
In geometry, the gyrate bidiminished rhombicosidodecahedron is one of the Johnson solids (J82).
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]
It can be constructed as a rhombicosidodecahedron with two non-opposing pentagonal cupolae (J5) removed and a third is rotated 36 degrees. Related Johnson solids are:
- The diminished rhombicosidodecahedron (J76) where one cupola is removed,
- The parabidiminished rhombicosidodecahedron (J80) where two opposing cupolae are removed,
- The metabidiminished rhombicosidodecahedron (J81) where two non-opposing cupolae are removed,
- And the tridiminished rhombicosidodecahedron (J83) where three cupolae are removed.
External links
- Weisstein, Eric W., "Gyrate bidiminished rhombicosidodecahedron" ("Johnson solid") at MathWorld.
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- elongated triangular pyramid
- elongated square pyramid
- elongated pentagonal pyramid
- gyroelongated square pyramid
- gyroelongated pentagonal pyramid
- triangular bipyramid
- pentagonal bipyramid
- elongated triangular bipyramid
- elongated square bipyramid
- elongated pentagonal bipyramid
- gyroelongated square bipyramid
- elongated triangular cupola
- elongated square cupola
- elongated pentagonal cupola
- elongated pentagonal rotunda
- gyroelongated triangular cupola
- gyroelongated square cupola
- gyroelongated pentagonal cupola
- gyroelongated pentagonal rotunda
- gyrobifastigium
- triangular orthobicupola
- square orthobicupola
- square gyrobicupola
- pentagonal orthobicupola
- pentagonal gyrobicupola
- pentagonal orthocupolarotunda
- pentagonal gyrocupolarotunda
- pentagonal orthobirotunda
- elongated triangular orthobicupola
- elongated triangular gyrobicupola
- elongated square gyrobicupola
- elongated pentagonal orthobicupola
- elongated pentagonal gyrobicupola
- elongated pentagonal orthocupolarotunda
- elongated pentagonal gyrocupolarotunda
- elongated pentagonal orthobirotunda
- elongated pentagonal gyrobirotunda
- gyroelongated triangular bicupola
- gyroelongated square bicupola
- gyroelongated pentagonal bicupola
- gyroelongated pentagonal cupolarotunda
- gyroelongated pentagonal birotunda
- augmented truncated tetrahedron
- augmented truncated cube
- biaugmented truncated cube
- augmented truncated dodecahedron
- parabiaugmented truncated dodecahedron
- metabiaugmented truncated dodecahedron
- triaugmented truncated dodecahedron
- gyrate rhombicosidodecahedron
- parabigyrate rhombicosidodecahedron
- metabigyrate rhombicosidodecahedron
- trigyrate rhombicosidodecahedron
- diminished rhombicosidodecahedron
- paragyrate diminished rhombicosidodecahedron
- metagyrate diminished rhombicosidodecahedron
- bigyrate diminished rhombicosidodecahedron
- parabidiminished rhombicosidodecahedron
- metabidiminished rhombicosidodecahedron
- gyrate bidiminished rhombicosidodecahedron
- tridiminished rhombicosidodecahedron
(See also List of Johnson solids, a sortable table)
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- ^ 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.
