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In geometry, the gyrate rhombicosidodecahedron is one of the Johnson solids (J 72).It is also a canonical polyhedron.. 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).
In geometry, the Rhombicosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces. It has 20 regular triangular faces, 30 square faces, 12 regular pentagonal faces, 60 vertices , and 120 edges .
In geometry, the gyrate bidiminished rhombicosidodecahedron is one of the Johnson solids (J 82). 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 ).
The criteria is also satisfied by eleven other Johnson solids, specifically the tridiminished icosahedron, parabidiminished rhombicosidodecahedron, tridiminished rhombicosidodecahedron, snub disphenoid, snub square antiprism, sphenocorona, sphenomegacorona, hebesphenomegacorona, disphenocingulum, bilunabirotunda, and triangular ...
Gyrate bidiminished rhombicosidodecahedron; Gyrate rhombicosidodecahedron; Gyrobifastigium; Gyroelongated pentagonal bicupola; Gyroelongated pentagonal birotunda; Gyroelongated pentagonal cupola; Gyroelongated pentagonal cupolarotunda; Gyroelongated pentagonal pyramid; Gyroelongated pentagonal rotunda; Gyroelongated square bicupola ...
Alternative Johnson solids, constructed by rotating different cupolae of a rhombicosidodecahedron, are: The gyrate rhombicosidodecahedron (J 72) where only one cupola is rotated; The metabigyrate rhombicosidodecahedron (J 74) where two non-opposing cupolae are rotated; And the trigyrate rhombicosidodecahedron (J 75) where three cupolae are rotated.
The parabidiminished rhombicosidodecahedron (J 80) where two opposing cupolae are removed, The gyrate bidiminished rhombicosidodecahedron (J 82) where two non-opposing cupolae are removed and a third is rotated 36 degrees, The tridiminished rhombicosidodecahedron (J 83) where three cupolae are removed.
In geometry, the metagyrate diminished rhombicosidodecahedron is one of the Johnson solids (J 78). It can be constructed as a rhombicosidodecahedron with one pentagonal cupola ( J 5 ) rotated through 36 degrees , and a non-opposing pentagonal cupola removed.