Concept
Diminished rhombicosidodecahedron
Related concepts (6)
Parabidiminished rhombicosidodecahedron
In geometry, the parabidiminished rhombicosidodecahedron is one of the Johnson solids (J_80). It is also a canonical polyhedron. It can be constructed as a rhombicosidodecahedron with two opposing pentagonal cupolae removed. Related Johnson solids are the diminished rhombicosidodecahedron (J_76) where one cupola is removed, the metabidiminished rhombicosidodecahedron (J_81) where two non-opposing cupolae are removed, and the tridiminished rhombicosidodecahedron (J_83) where three cupolae are removed.
Metabidiminished rhombicosidodecahedron
In geometry, the metabidiminished rhombicosidodecahedron is one of the Johnson solids (J_81). It can be constructed as a rhombicosidodecahedron with two non-opposing pentagonal cupolae (J_5) removed. Related Johnson solids are: The diminished rhombicosidodecahedron (J_76) where one cupola is removed, 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, And the tridiminished rhombicosidodecahedron (J_83) where three cupolae are removed.
Tridiminished rhombicosidodecahedron
In geometry, the tridiminished rhombicosidodecahedron is one of the Johnson solids (J_83). It can be constructed as a rhombicosidodecahedron with three pentagonal cupolae removed. Related Johnson solids are: J_76: diminished rhombicosidodecahedron with one cupola removed, J_80: parabidiminished rhombicosidodecahedron with two opposing cupolae removed, and J_81: metabidiminished rhombicosidodecahedron with two non-opposing cupolae removed.
Gyrate bidiminished rhombicosidodecahedron
In geometry, the gyrate bidiminished rhombicosidodecahedron is one of the Johnson solids (J_82). It can be constructed as a rhombicosidodecahedron with two non-opposing pentagonal cupolae (J_5) removed and a third is rotated 36 degrees. Related Johnson solids are: The diminished rhombicosidodecahedron (J_76) where one cupola is removed, The parabidiminished rhombicosidodecahedron (J_80) where two opposing cupolae are removed, The metabidiminished rhombicosidodecahedron (J_81) where two non-opposing cupolae are removed, And the tridiminished rhombicosidodecahedron (J_83) where three cupolae are removed.
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".