Coxeter notation

Fundamental domains of reflective 3D point groups

, [ ] = [1] C1v	, [2] C2v	, [3] C3v	, [4] C4v	, [5] C5v	, [6] C6v
Order 2	Order 4	Order 6	Order 8	Order 10	Order 12
[2] = [2,1] D1h	[2,2] D2h	[2,3] D3h	[2,4] D4h	[2,5] D5h	[2,6] D6h
Order 4	Order 8	Order 12	Order 16	Order 20	Order 24
, [3,3], Td		, [4,3], Oh		, [5,3], Ih
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 [ ]×[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.