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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 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, a truncated icosidodecahedron, rhombitruncated icosidodecahedron, [1] great rhombicosidodecahedron, [2] [3] omnitruncated dodecahedron or omnitruncated icosahedron [4] is an Archimedean solid, one of thirteen convex, isogonal, non-prismatic solids constructed by two or more types of regular polygon faces.
(quasi-regular: vertex- and edge-uniform) 32: 20 triangles 12 pentagons: 60: 30 3,5,3,5 truncated dodecahedron : 32: 20 triangles 12 decagons: 90 60 3,10,10 truncated icosahedron or commonly football (soccer ball) 32: 12 pentagons 20 hexagons: 90 60 5,6,6 rhombicosidodecahedron or small rhombicosidodecahedron 62: 20 triangles 30 squares
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 ...
Cartesian coordinates for the vertices of a uniform great rhombicosidodecahedron are all the even permutations of (±1/τ 2 , 0, ±τ 2 ) (±1, ±1, ± √ 5 )
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 ).
It shares its vertex arrangement with the truncated great dodecahedron and the uniform compounds of 6 or 12 pentagonal prisms.It additionally shares its edge arrangement with the nonconvex great rhombicosidodecahedron (having the square faces in common), and with the great dodecicosidodecahedron (having the decagrammic faces in common).