Compound of five octahedra

<table><tbody><tr><th colspan="2">Compound of five octahedra</th></tr><tr><td colspan="2">(see here for a 3D model)</td></tr><tr><td>Type</td><td><a href="/facts/Regular_polyhedral_compound/L13pItNN">Regular compound</a></td></tr><tr><td>Index</td><td>UC17, W23</td></tr><tr><td>Coxeter symbol</td><td>[5{3,4}]2{3,5}</td></tr><tr><td><a href="/facts/Euler_characteristic/JCjzWUr2">Elements</a>(As a compound)</td><td>5 <a href="/facts/Octahedron/G38q92xW">octahedra</a>:<i>F</i> = 40, <i>E</i> = 60, <i>V</i> = 30</td></tr><tr><td><a href="/facts/Dual_polyhedron/rkIHbmAf">Dual compound</a></td><td><a href="/facts/Compound_of_five_cubes/PNIAfKTN">Compound of five cubes</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 compound of five octahedra is one of the five regular <a href="/facts/Polyhedron_compound/L13pItNN">polyhedron compounds</a>, and can also be seen as a <a href="/facts/Stellation/T7NY6CWv">stellation</a>. It was first described by <a href="/facts/Edmund_Hess/HJdajw7h">Edmund Hess</a> in 1876. It is unique among the regular compounds for not having a regular convex hull. It can also be called a small icosicosahedron.
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Compound of five octahedra open-in-new

Compound of five octahedra