Concept
Gyrate rhombicosidodecahedron
Related concepts (5)
Trigyrate rhombicosidodecahedron
In geometry, the trigyrate rhombicosidodecahedron is one of the Johnson solids (J_75). It contains 20 triangles, 30 squares and 12 pentagons. It is also a canonical polyhedron. It can be constructed as a rhombicosidodecahedron with three pentagonal cupolae rotated through 36 degrees. Related Johnson solids are: The gyrate rhombicosidodecahedron (J_72) where one cupola is rotated; The parabigyrate rhombicosidodecahedron (J_73) where two opposing cupolae are rotated; And the metabigyrate rhombicosidodecahedron (J_74) where two non-opposing cupolae are rotated.
Parabigyrate rhombicosidodecahedron
In geometry, the parabigyrate rhombicosidodecahedron is one of the Johnson solids (J_73). It can be constructed as a rhombicosidodecahedron with two opposing pentagonal cupolae rotated through 36 degrees. It is also a canonical polyhedron. 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.
Metabigyrate rhombicosidodecahedron
In geometry, the metabigyrate rhombicosidodecahedron is one of the Johnson solids (J_74). It can be constructed as a rhombicosidodecahedron with two non-opposing pentagonal cupolae rotated through 36 degrees. It is also a canonical polyhedron. Alternative Johnson solids, constructed by rotating different cupolae of a rhombicosidodecahedron, are: The gyrate rhombicosidodecahedron (J_72) where only one cupola is rotated; The parabigyrate rhombicosidodecahedron (J_73) where two opposing cupolae are rotated; And the trigyrate rhombicosidodecahedron (J_75) where three cupolae are rotated.
Rhombicosidodecahedron
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. Johannes Kepler in Harmonices Mundi (1618) named this polyhedron a rhombicosidodecahedron, being short for truncated icosidodecahedral rhombus, with icosidodecahedral rhombus being his name for a rhombic triacontahedron.
Johnson solid
In geometry, a Johnson solid is a strictly convex polyhedron each face of which is a regular polygon. There is no requirement that each face must be the same polygon, or that the same polygons join around each vertex. An example of a Johnson solid is the square-based pyramid with equilateral sides (J_1); it has 1 square face and 4 triangular faces. Some authors require that the solid not be uniform (i.e., not Platonic solid, Archimedean solid, uniform prism, or uniform antiprism) before they refer to it as a "Johnson solid".