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Compound of five cubes
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<table><tbody><tr><th colspan="2">Compound of five cubes</th></tr><tr><td colspan="2">(Animation, 3D model)</td></tr><tr><td>Type</td><td><a href="/facts/Regular_polyhedral_compound/L13pItNN">Regular compound</a></td></tr><tr><td>Coxeter symbol</td><td>2{5,3}[5{4,3}]</td></tr><tr><td><a href="/facts/Stellation/T7NY6CWv">Stellation</a> core</td><td><a href="/facts/Rhombic_triacontahedron/HmHWG8JY">rhombic triacontahedron</a></td></tr><tr><td><a href="/facts/Convex_hull/D4Id3JDS">Convex hull</a></td><td><a href="/facts/Dodecahedron/7r519eCl">Dodecahedron</a></td></tr><tr><td>Index</td><td>UC9</td></tr><tr><td>Polyhedra</td><td>5 <a href="/facts/Cube/65lUaAqN">cubes</a></td></tr><tr><td>Faces</td><td>30 <a href="/facts/Square_(geometry)/JHJeMvmL">squares</a> (visible as 360 <a href="/facts/Triangle/cRXUwsMn">triangles</a>)</td></tr><tr><td>Edges</td><td>60</td></tr><tr><td>Vertices</td><td>20</td></tr><tr><td>Dual</td><td><a href="/facts/Compound_of_five_octahedra/8M825cd5">Compound of five octahedra</a></td></tr><tr><td><a href="/facts/Symmetry_group/CNqeseMp">Symmetry group</a></td><td><a href="/facts/Icosahedral_symmetry/pDlwAy23">icosahedral</a> (<i>I</i>h)</td></tr><tr><td><a href="/facts/Subgroup/r91mBgpa">Subgroup</a> restricting to one constituent</td><td><a href="/facts/Tetrahedral_symmetry/hIVlf9pu">pyritohedral</a> (<i>T</i>h)</td></tr></tbody></table> <p>The <a href="/facts/Polyhedral_compound/L13pItNN">compound</a> of five <a href="/facts/Cube/65lUaAqN">cubes</a> is one of the five <a href="/facts/Polyhedral_compound/L13pItNN">regular polyhedral compounds</a>. It was first described by <a href="/facts/Edmund_Hess/HJdajw7h">Edmund Hess</a> in 1876. </p><p>Its vertices are those of a regular <a href="/facts/Dodecahedron/7r519eCl">dodecahedron</a>. Its edges form <a href="/facts/Pentagram/cN0ke8tp">pentagrams</a>, which are the <a href="/facts/Stellation/T7NY6CWv">stellations</a> of the pentagonal faces of the dodecahedron. </p><p>It is one of the stellations of the <a href="/facts/Rhombic_triacontahedron/HmHWG8JY">rhombic triacontahedron</a>. Its dual is the <a href="/facts/Compound_of_five_octahedra/8M825cd5">compound of five octahedra</a>. It has <a href="/facts/Icosahedral_symmetry/pDlwAy23">icosahedral symmetry</a> (Ih). </p>