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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.
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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.
Rhombitruncated icosidodecahedron Truncated icosidodecahedron Snub dodecahedron Snid V 60,E 150,F 92=(20+60){3}+12{5}
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Rhombitruncated icosidodecahedron Truncated icosidodecahedron Great truncated icosidodecahedron Gaquatid V 120,E 180,F 62=30{4}+20{6}+12{10/3}
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 rhombicuboctahedron is an Archimedean solid with 26 faces, consisting of 8 equilateral triangles and 18 squares. It was named by Johannes Kepler in his 1618 Harmonices Mundi, being short for truncated cuboctahedral rhombus, with cuboctahedral rhombus being his name for a rhombic dodecahedron.