Lemoine hexagon the Lemoine hexagon is known as the first Lemoine circle. Lemoine hexagon In geometry, the Lemoine hexagon is a cyclic hexagon with vertices given by the six intersections of the edges of a triangle and the three lines that are parallel to the edges that pass through its symmedian point. There are two definitions of the hexagon that differ based on the order in which the vertices are connected. The Lemoine hexagon can be drawn defined in two ways, first as a simple hexagon with vertices at the intersections as defined before. The second is a self-intersecting hexagon with the
Plane of rotation two points, one on each of the planes. A double rotation has two angles of rotation, one for each plane of rotation. The rotation is specified by giving the two planes and two non-zero angles, and (if either angle is zero the rotation is simple). Points in the first plane rotate through , while points in the second plane rotate through . All other points rotate through an angle between and , so in a sense they together determine the amount of rotation. For a general double rotation the planes of rotation and angles are unique, and given a general