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
A Plane Is Born Mark visits the Popular Flying Association Rally at Cranfield to see some of the 3000 or so home-built and vintage aircraft that have flown in for the weekend. He talks to Graham Newby, the Chairman of the PFA and the Editor of Flyer Magazine who takes him through the perils and pit falls of building his own plane. - Test Flight Mark travels to the Europa Factory in North Yorkshire where after seeing all the components that go into making a kit, he takes a test flight with Technical Director Andy Draper. In part 2, he starts his private pilot