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Small complex icosidodecahedron
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<table><tbody><tr><th colspan="2">Small complex icosidodecahedron</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> = 32, <i>E</i> = 60 (30x2)<i>V</i> = 12 (χ = −16)</td></tr><tr><td>Faces by sides</td><td>20{3}+12{5}</td></tr><tr><td><a href="/facts/Coxeter_diagram/Ik6LmXJB">Coxeter diagram</a></td><td></td></tr><tr><td><a href="/facts/Wythoff_symbol/ECD0Wl5x">Wythoff symbol</a></td><td>5 | 3/2 5</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>-, <a href="/facts/Harold_Scott_MacDonald_Coxeter/D2l5jWGG">C</a>-, <a href="/facts/List_of_Wenninger_polyhedron_models/hwApnNpt">W</a>-</td></tr><tr><td>Dual polyhedron</td><td><a href="/facts/Small_complex_icosidodecacron/c4zVP1dT">Small complex icosidodecacron</a></td></tr><tr><td>Vertex figure</td><td>(3/2.5)5(3.5)5/3</td></tr><tr><td>Bowers acronym</td><td>Cid</td></tr></tbody></table> <p>In <a href="/facts/Geometry/wTQf5ffQ">geometry</a>, the small complex icosidodecahedron is a degenerate <a href="/facts/Uniform_star_polyhedron/rSv9XpHQ">uniform star polyhedron</a>. Its edges are doubled, making it degenerate. The star has 32 faces (20 <a href="/facts/Triangle/cRXUwsMn">triangles</a> and 12 <a href="/facts/Pentagon/xoq5oJeQ">pentagons</a>), 60 (doubled) edges and 12 vertices and 4 sharing faces. The faces in it are considered as two overlapping edges as topological polyhedron. </p><p>A small complex icosidodecahedron can be <a href="/facts/Wythoff_construction/8yTYjp5e">constructed</a> from a number of different <a href="/facts/Vertex_figure/3u2ySK0C">vertex figures</a>. </p><p>A very similar figure emerges as a geometrical truncation of the <a href="/facts/Great_stellated_dodecahedron/7efrgSub">great stellated dodecahedron</a>, where the pentagram faces become doubly-wound pentagons ({5/2} --> {10/2}), making the internal pentagonal planes, and the three meeting at each vertex become triangles, making the external triangular planes. </p>