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In geometry, the truncated rhombicosidodecahedron is a polyhedron, constructed as a truncated rhombicosidodecahedron. It has 122 faces: 12 decagons, 30 octagons, 20 hexagons, and 60 squares. It has 122 faces: 12 decagons, 30 octagons, 20 hexagons, and 60 squares.
The rhombicosidodecahedron shares the vertex arrangement with the small stellated truncated dodecahedron, and with the uniform compounds of six or twelve pentagrammic prisms. The Zometool kits for making geodesic domes and other polyhedra use slotted balls as connectors.
The truncated icosidodecahedron is the convex hull of a rhombicosidodecahedron with cuboids above its 30 squares, whose height to base ratio is φ. The rest of its space can be dissected into nonuniform cupolas, namely 12 between inner pentagons and outer decagons and 20 between inner triangles and outer hexagons .
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.
In geometry, the metabidiminished rhombicosidodecahedron is one of the Johnson solids (J 81). 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 ).
Truncated icosidodecahedron - An Archimedean solid, with Schläfli symbol t 0,1,2 {5,3}. Nonconvex great rhombicosidodecahedron - a nonconvex uniform polyhedron, with Schläfli symbol t 0,2 {5/3,3}. Topics referred to by the same term
The truncated rhombicuboctahedron is a polyhedron, constructed as a truncation of the rhombicuboctahedron. It has 50 faces consisting of 18 octagons, 8 hexagons, and 24 squares. It can fill space with the truncated cube, truncated tetrahedron and triangular prism as a truncated runcic cubic honeycomb.
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.