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
Shoulder plane for joinery. Unlike the rebate plane, the shoulder plane is intended to cut end grain. There are therefore differences between it and a rebate plane in the angles at which the iron (blade) is set. A shoulder plane also has a much finer set mouth, which allows finer shavings to be taken. Shoulder plane The shoulder plane (also bullnose plane) is a plane tool with a blade flush with the edges of the plane, allowing trimming right up to the edge of a workpiece. Like a rebate plane, the shoulder plane's blade extends, therefore cuts, to the full width of