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
Winter Hexagon Winter Hexagon The Winter Hexagon or Winter Circle/Oval is an asterism appearing to be in the form of a hexagon with vertices at Rigel, Aldebaran, Capella, Pollux, Procyon, and Sirius. It is mostly upon the Northern Hemisphere's celestial sphere. On most locations on Earth (except the South Island of New Zealand and the south of Chile and Argentina and further south), this asterism is prominently in the sky from approximately December to March. In the tropics and southern hemisphere, this (then called "summer hexagon") can be extended with the bright star Canopus in the south. Smaller and more regularly shaped