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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 .
Only a few uniform polytopes have this property, including the four-dimensional 600-cell, the three-dimensional icosidodecahedron, and the two-dimensional decagon. (The icosidodecahedron is the equatorial cross-section of the 600-cell, and the decagon is the equatorial cross-section of the icosidodecahedron.)
It can be used to define the rhombohedral lattice system, a honeycomb with rhombohedral cells. A rhombohedron has two opposite apices at which all face angles are equal; a prolate rhombohedron has this common angle acute, and an oblate rhombohedron has an obtuse angle at these vertices.
As Johannes Kepler noted in his 1611 book on snowflakes (Strena seu de Nive Sexangula), honey bees use the geometry of rhombic dodecahedra to form honeycombs from a tessellation of cells each of which is a hexagonal prism capped with half a rhombic dodecahedron. The rhombic dodecahedron also appears in the unit cells of diamond and diamondoids ...
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 ).
This polyhedron is related to the nonconvex great rhombicosidodecahedron (quasirhombicosidodecahedron) by a branched cover: there is a function from the great dirhombicosidodecahedron to the quasirhombicosidodecahedron that is 2-to-1 everywhere, except for the vertices. [2]
Nonconvex great rhombicosidodecahedron - a nonconvex uniform polyhedron, with Schläfli symbol t 0,2 {5/3,3}. Topics referred to by the same term This disambiguation page lists articles associated with the title Great rhombicosidodecahedron .