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Small dodecahemidodecahedron
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<table><tbody><tr><th colspan="2">Small dodecahemidodecahedron</th></tr><tr><td colspan="2"></td></tr><tr><td>Type</td><td><a href="/facts/Uniform_star_polyhedron/rSv9XpHQ">Uniform star polyhedron</a></td></tr><tr><td><a href="/facts/Euler_characteristic/JCjzWUr2">Elements</a></td><td><i>F</i> = 18, <i>E</i> = 60<i>V</i> = 30 (χ = −12)</td></tr><tr><td>Faces by sides</td><td>12{5}+6{10}</td></tr><tr><td><a href="/facts/Coxeter_diagram/Ik6LmXJB">Coxeter diagram</a></td><td> (double covering)</td></tr><tr><td><a href="/facts/Wythoff_symbol/ECD0Wl5x">Wythoff symbol</a></td><td>5/4 5 | 5 (double covering)</td></tr><tr><td><a href="/facts/List_of_spherical_symmetry_groups/3X3YcHoQ">Symmetry group</a></td><td>Ih, [5,3], *532</td></tr><tr><td><a href="/facts/List_of_uniform_polyhedra/robWbdeH">Index references</a></td><td><a href="/facts/Uniform_polyhedron/PHnprqRC">U</a>51, <a href="/facts/Harold_Scott_MacDonald_Coxeter/D2l5jWGG">C</a>65, <a href="/facts/List_of_Wenninger_polyhedron_models/hwApnNpt">W</a>91</td></tr><tr><td>Dual polyhedron</td><td><a href="/facts/Small_dodecahemidodecacron/luTu98g8">Small dodecahemidodecacron</a></td></tr><tr><td>Vertex figure</td><td>5.10.5/4.10</td></tr><tr><td>Bowers acronym</td><td>Sidhid</td></tr></tbody></table> <p>In <a href="/facts/Geometry/wTQf5ffQ">geometry</a>, the small dodecahemidodecahedron is a <a href="/facts/Nonconvex_uniform_polyhedron/rSv9XpHQ">nonconvex uniform polyhedron</a>, indexed as U51. It has 18 faces (12 <a href="/facts/Pentagon/xoq5oJeQ">pentagons</a> and 6 <a href="/facts/Decagon/GdHnJjMK">decagons</a>), 60 <a href="/facts/Edge_(geometry)/3lFN6sEz">edges</a>, and 30 <a href="/facts/Vertex_(geometry)/ID3cea9z">vertices</a>. Its <a href="/facts/Vertex_figure/3u2ySK0C">vertex figure</a> alternates two regular <a href="/facts/Pentagon/xoq5oJeQ">pentagons</a> and <a href="/facts/Decagon/GdHnJjMK">decagons</a> as a <a href="/facts/Antiparallelogram/QDzKogA3">crossed quadrilateral</a>. </p><p>It is a <a href="/facts/Hemipolyhedron/SLbcVFjT">hemipolyhedron</a> with six decagonal faces passing through the model center. </p>