Hexagon has no degrees of freedom but can seen as directed edges. Hexagons of symmetry g2, i4, and r12, as parallelogons can tessellate the Euclidean plane by translation. Other hexagon shapes can tile the plane with different orientations. The 6 roots of the simple Lie group , represented by a Dynkin diagram , are in a regular hexagonal pattern. The two simple roots have a 120° angle between them. The 12 roots of the Exceptional Lie group G2, represented by a Dynkin diagram are also in a hexagonal pattern. The two simple roots of two lengths have a 150° angle between
Magic hexagon Magic hexagon A magic hexagon of order "n" is an arrangement of numbers in a centered hexagonal pattern with "n" cells on each edge, in such a way that the numbers in each row, in all three directions, sum to the same magic constant "M". A normal magic hexagon contains the consecutive integers from 1 to 3"n" − 3"n" + 1. It turns out that normal magic hexagons exist only for "n" = 1 (which is trivial, as it is composed of only 1 hexagon) and "n" = 3. Moreover, the solution of order 3 is essentially unique. Meng also