Menu
Home
People
Places
Arts
History
Plants & Animals
Science
Life & Culture
Technology
Reference.org
Compound of five tetrahedra
open-in-new
<table><tbody><tr><th colspan="2">Compound of five tetrahedra</th></tr><tr><td colspan="2"></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>{5,3}[5{3,3}] {3,5}</td></tr><tr><td>Index</td><td>UC5, <a href="/facts/List_of_Wenninger_polyhedron_models/hwApnNpt">W24</a></td></tr><tr><td><a href="/facts/Euler_characteristic/JCjzWUr2">Elements</a>(As a compound)</td><td>5 <a href="/facts/Tetrahedron/7mkSrl6j">tetrahedra</a>:<i>F</i> = 20, <i>E</i> = 30, <i>V</i> = 20</td></tr><tr><td><a href="/facts/Dual_polyhedron/rkIHbmAf">Dual compound</a></td><td>Self-dual</td></tr><tr><td><a href="/facts/Symmetry_group/CNqeseMp">Symmetry group</a></td><td><a href="/facts/Chirality_(mathematics)/FtKNlHTb">chiral</a> <a href="/facts/Icosahedral_symmetry/pDlwAy23">icosahedral</a> (<i>I</i>)</td></tr><tr><td><a href="/facts/Subgroup/r91mBgpa">Subgroup</a> restricting to one constituent</td><td><a href="/facts/Chirality_(mathematics)/FtKNlHTb">chiral</a> <a href="/facts/Tetrahedral_symmetry/hIVlf9pu">tetrahedral</a> (<i>T</i>)</td></tr></tbody></table> <p>The <a href="/facts/Polyhedral_compound/L13pItNN">compound</a> of five <a href="/facts/Tetrahedron/7mkSrl6j">tetrahedra</a> is one of the five regular polyhedral compounds. This <a href="/facts/Polyhedral_compound/L13pItNN">compound</a> <a href="/facts/Polyhedron/UC0p9FTF">polyhedron</a> is also a <a href="/facts/Stellation/T7NY6CWv">stellation</a> of the regular <a href="/facts/Icosahedron/wWbpnDYp">icosahedron</a>. It was first described by <a href="/facts/Edmund_Hess/HJdajw7h">Edmund Hess</a> in 1876. </p><p>It can be seen as a faceting of a <a href="/facts/Regular_dodecahedron/xClYqhcp">regular dodecahedron</a>. </p>