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Alternatively, if you expand each of five cubes by moving the faces away from the origin the right amount and rotating each of the five 72° around so they are equidistant from each other, without changing the orientation or size of the faces, and patch the pentagonal and triangular holes in the result, you get a rhombicosidodecahedron ...
In geometry, the parabidiminished rhombicosidodecahedron is one of the Johnson solids (J 80). 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 tridiminished rhombicosidodecahedron is one of the Johnson solids (J 83). It can be constructed as a rhombicosidodecahedron with three pentagonal cupolae removed. 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 ...
3D model of a nonconvex great rhombicosidodecahedron. In geometry, the nonconvex great rhombicosidodecahedron is a nonconvex uniform polyhedron, indexed as U 67. It has 62 faces (20 triangles, 30 squares and 12 pentagrams), 120 edges, and 60 vertices. [1] It is also called the quasirhombicosidodecahedron. It is given a Schläfli symbol rr{5 ...
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.
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 diminished rhombicosidodecahedron is one of the Johnson solids (J 76).It can be constructed as a rhombicosidodecahedron with one pentagonal cupola removed.. 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 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 ).