illusion or rhombicosidodecahedrona Rhombicosidodecahedron Rhombicosidodecahedron.jpg Type Archimedean solid Uniform polyhedron Elements F = 62, E = 120, V = 60 (χ = 2) Faces by sides 20{3}+30{4}+12{5} Conway notation eD or aaD Schläfli symbols rr{5,3} or � { 5 3 } r{\begin{Bmatrix}5\\3\end{Bmatrix}} t0,2{5,3} Wythoff symbol 3 5 | 2 Coxeter diagram CDel node 1.pngCDel 5.pngCDel node.pngCDel 3.pngCDel node 1.png Symmetry group Ih, H3, [5,3], (*532), order 120 Rotation group I, [5,3]+, (532), order 60 Dihedral angle 3-4: 159°05′41″ (159.09°) 4-5: 148°16′57″ (148.28°) References U27, C30, W14 Properties Semiregular convex Polyhedron small rhombi 12-20 max.png Colored faces Polyhedron small rhombi 12-20 vertfig.svg 3.4.5.4 (Vertex figure) Polyhedron small rhombi 12-20 dual max.png Deltoidal hexecontahedron (dual polyhedron) Polyhedron small rhombi 12-20 net.svg Net In geometry, the rhombicosidodecahedron, or Rectified Rhombic Triacontahedron, 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. Names 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.triacontahedron into a It can also be called an expanded or cantellated dodecahedron or icosahedron, from truncation operations on either uniform polyhedron. Dimensions For a rhombicosidodecahedron with edge length a, its surface area and volume are: � = ( Geometric relationsAlternatively, if you expand each of
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