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Coxeter notation
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Fundamental domains of reflective 3D point groups<table><tbody><tr><th>, [ ] = [1]C1v</th><th>, [2]C2v</th><th>, [3]C3v</th><th>, [4]C4v</th><th>, [5]C5v</th><th>, [6]C6v</th></tr><tr><td>Order 2</td><td>Order 4</td><td>Order 6</td><td>Order 8</td><td>Order 10</td><td>Order 12</td></tr><tr><th>[2] = [2,1]D1h</th><th>[2,2]D2h</th><th>[2,3]D3h</th><th>[2,4]D4h</th><th>[2,5]D5h</th><th>[2,6]D6h</th></tr><tr><td>Order 4</td><td>Order 8</td><td>Order 12</td><td>Order 16</td><td>Order 20</td><td>Order 24</td></tr><tr><th colspan="2">, [3,3], <a href="/facts/Tetrahedral_symmetry/hIVlf9pu">Td</a></th><th colspan="2">, [4,3], <a href="/facts/Octahedral_symmetry/qLqhYxgm">Oh</a></th><th colspan="2">, [5,3], <a href="/facts/Icosahedral_symmetry/pDlwAy23">Ih</a></th></tr><tr><td colspan="2">Order 24</td><td colspan="2">Order 48</td><td colspan="2">Order 120</td></tr><tr><td colspan="6">Coxeter notation expresses <a href="/facts/Coxeter_group/bgzHFm1Q">Coxeter groups</a> as a list of branch orders of a <a href="/facts/Coxeter_diagram/Ik6LmXJB">Coxeter diagram</a>, like the <a href="/facts/Polyhedral_groups/ynwsQLXE">polyhedral groups</a>, = [p,q]. <a href="/facts/Dihedral_symmetry_in_three_dimensions/xNRpsIAF">Dihedral groups</a>, , can be expressed as a product [ ]×[<i>n</i>] or in a single symbol with an explicit order 2 branch, [2,<i>n</i>].</td></tr></tbody></table> <p>In <a href="/facts/Geometry/wTQf5ffQ">geometry</a>, Coxeter notation (also Coxeter symbol) is a system of classifying <a href="/facts/Symmetry_group/CNqeseMp">symmetry groups</a>, describing the angles between fundamental reflections of a <a href="/facts/Coxeter_group/bgzHFm1Q">Coxeter group</a> in a bracketed notation expressing the structure of a <a href="/facts/Coxeter-Dynkin_diagram/Ik6LmXJB">Coxeter-Dynkin diagram</a>, with modifiers to indicate certain subgroups. The notation is named after <a href="/facts/H._S._M._Coxeter/D2l5jWGG">H. S. M. Coxeter</a>, and has been more comprehensively defined by <a href="/facts/Norman_Johnson_(mathematician)/bQtL9w56">Norman Johnson</a>. </p>