Coxeter notation

Fundamental domains of reflective 3D point groups
, $[ ] = [1] C 1v$	, $[2] C 2v$	, $[3] C 3v$	, $[4] C 4v$	, $[5] C 5v$	, $[6] C 6v$
Order 2	Order 4	Order 6	Order 8	Order 10	Order 12
$[2] = [2,1] D 1h$	$[2,2] D 2h$	$[2,3] D 3h$	$[2,4] D 4h$	$[2,5] D 5h$	$[2,6] D 6h$
Order 4	Order 8	Order 12	Order 16	Order 20	Order 24
, $[3,3], T d$		, $[4,3], O h$		, $[5,3], I h$
Order 24		Order 48		Order 120
Coxeter notation expresses Coxeter groups as a list of branch orders of a Coxeter diagram, like the polyhedral groups, $= [p,q]$ . Dihedral groups, , can be expressed as a product $[ ]\times[n]$ or in a single symbol with an explicit order 2 branch, $[2, n]$ .

In geometry, Coxeter notation (also Coxeter symbol) is a system of classifying symmetry groups, describing the angles between fundamental reflections of a Coxeter group in a bracketed notation expressing the structure of a Coxeter-Dynkin diagram, with modifiers to indicate certain subgroups. The notation is named after H. S. M. Coxeter, and has been more comprehensively defined by Norman Johnson.