Menu
Home
People
Places
Arts
History
Plants & Animals
Science
Life & Culture
Technology
Reference.org
Rhombicosidodecahedron
open-in-new
<table><tbody><tr><th colspan="2">Rhombicosidodecahedron</th></tr><tr><td colspan="2">(Click here for rotating model)</td></tr><tr><td>Type</td><td><a href="/facts/Archimedean_solid/wYWeHDYT">Archimedean solid</a><a href="/facts/Uniform_polyhedron/PHnprqRC">Uniform polyhedron</a></td></tr><tr><td><a href="/facts/Euler_characteristic/JCjzWUr2">Elements</a></td><td><i>F</i> = 62, <i>E</i> = 120, <i>V</i> = 60 (χ = 2)</td></tr><tr><td>Faces by sides</td><td>20{3}+30{4}+12{5}</td></tr><tr><td><a href="/facts/Conway_polyhedron_notation/MVmYMqID">Conway notation</a></td><td>eD or aaD</td></tr><tr><td rowspan="2"><a href="/facts/Schl%25C3%25A4fli_symbol/jNQR77UU">Schläfli symbols</a></td><td>rr{5,3} or r { 5 3 } {\displaystyle r{\begin{Bmatrix}5\\3\end{Bmatrix}}} </td></tr><tr><td>t0,2{5,3}</td></tr><tr><td><a href="/facts/Wythoff_symbol/ECD0Wl5x">Wythoff symbol</a></td><td>3 5 | 2</td></tr><tr><td><a href="/facts/Coxeter_diagram/Ik6LmXJB">Coxeter diagram</a></td><td></td></tr><tr><td><a href="/facts/List_of_spherical_symmetry_groups/3X3YcHoQ">Symmetry group</a></td><td><a href="/facts/Icosahedral_symmetry/pDlwAy23">Ih</a>, H3, [5,3], (*532), order 120</td></tr><tr><td><a href="/facts/Point_groups_in_three_dimensions/Uc4MRIyl">Rotation group</a></td><td><a href="/facts/Icosahedral_symmetry/pDlwAy23">I</a>, [5,3]+, (532), order 60</td></tr><tr><td><a href="/facts/Dihedral_angle/C9WEJsuS">Dihedral angle</a></td><td>3-4: 159°05′41″ (159.09°)4-5: 148°16′57″ (148.28°)</td></tr><tr><td><a href="/facts/List_of_uniform_polyhedra/robWbdeH">References</a></td><td><a href="/facts/Uniform_polyhedron/PHnprqRC">U</a>27, <a href="/facts/Harold_Scott_MacDonald_Coxeter/D2l5jWGG">C</a>30, <a href="/facts/List_of_Wenninger_polyhedron_models/hwApnNpt">W</a>14</td></tr><tr><td>Properties</td><td>Semiregular <a href="/facts/Convex_polyhedron/2pRHcRgC">convex</a></td></tr><tr><td>Colored faces</td><td>3.4.5.4(<a href="/facts/Vertex_figure/3u2ySK0C">Vertex figure</a>)</td></tr><tr><td><a href="/facts/Deltoidal_hexecontahedron/IWvmY471">Deltoidal hexecontahedron</a>(<a href="/facts/Dual_polyhedron/rkIHbmAf">dual polyhedron</a>)</td><td><a href="/facts/Net_(polyhedron)/lU8fmGJs">Net</a></td></tr></tbody></table> <p>In <a href="/facts/Geometry/wTQf5ffQ">geometry</a>, the rhombicosidodecahedron is an <a href="/facts/Archimedean_solid/wYWeHDYT">Archimedean solid</a>, one of thirteen <a href="/facts/Convex_polyhedron/2pRHcRgC">convex</a> <a href="/facts/Isogonal_figure/5nC8PdBm">isogonal</a> nonprismatic solids constructed of two or more types of <a href="/facts/Regular_polygon/ws89Nhpt">regular polygon</a> <a href="/facts/Face_(geometry)/T2E6BTU4">faces</a>. </p><p>It has a total of 62 faces: 20 regular <a href="/facts/Triangular/cRXUwsMn">triangular</a> faces, 30 <a href="/facts/Square_(geometry)/JHJeMvmL">square</a> faces, 12 regular <a href="/facts/Pentagon/xoq5oJeQ">pentagonal</a> faces, with 60 <a href="/facts/Vertex_(geometry)/ID3cea9z">vertices</a>, and 120 <a href="/facts/Edge_(geometry)/3lFN6sEz">edges</a>. </p>