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Truncated icosidodecahedron
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{{short description|Archimedean solid}} {{Semireg polyhedra db|Semireg polyhedron stat table|grID}} In [[geometry]], a '''truncated icosidodecahedron''', '''rhombitruncated icosidodecahedron''',<ref name="wenninger16">Wenninger Model Number 16</ref> '''great rhombicosidodecahedron''',<ref name="williams94">Williams (Section 3-9, p. 94)</ref><ref name="cromwell82">Cromwell (p. 82)</ref> '''omnitruncated dodecahedron''' or '''omnitruncated icosahedron'''<ref name="johnson1966">Norman Woodason Johnson, "The Theory of Uniform Polytopes and Honeycombs", 1966</ref> is an [[Archimedean solid]], one of thirteen [[Convex polytope|convex]], [[Isogonal figure|isogonal]], non-[[Prism (geometry)|prismatic]] solids constructed by two or more types of [[regular polygon|regular]] polygon [[Face (geometry)|face]]s. It has 62 faces: 30 [[square (geometry)|squares]], 20 regular [[hexagon]]s, and 12 regular [[decagon]]s. It has the most edges and vertices of all [[Platonic solid|Platonic]] and Archimedean solids, though the [[snub dodecahedron]] has more faces. Of all vertex-transitive polyhedra, it occupies the largest percentage (89.80%) of the volume of a [[Circumscribed sphere|sphere]] in which it is [[inscribed]], very narrowly beating the snub dodecahedron (89.63%) and small [[rhombicosidodecahedron]] (89.23%), and less narrowly beating the [[truncated icosahedron]] (86.74%); it also has by far the greatest volume (206.8 cubic units) when its edge length equals 1. Of all [[vertex-transitive]] polyhedra that are not prisms or [[antiprism]]s, it has the largest sum of angles (90 + 120 + 144 = 354 degrees) at each vertex; only a prism or antiprism with more than 60 sides would have a larger sum. Since each of its faces has [[point symmetry]] (equivalently, 180Β° [[rotational symmetry]]), the truncated icosidodecahedron is a '''15'''-[[zonohedron]].
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