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
Distance from a point to a plane the point on a plane formula_33 closest to an arbitrary point formula_34 is formula_2 given by where and the distance from the point to the plane is Distance from a point to a plane In Euclidean space, the point on a plane formula_1 that is closest to the origin has the Cartesian coordinates formula_2, where The distance between the origin and point formula_2 is formula_5. If what is desired is the distance from a point not at the origin to the nearest point on a plane, this can be found by a change of variables that moves the origin to