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
Real projective plane of the (equivalent) ordinary disk are identified with each other; this is how a real projective plane is formed out of a disk. Therefore the surface shown in Figure 1 (cross-cap with disk) is topologically equivalent to the real projective plane "RP". The points in the plane can be represented by homogeneous coordinates. A point has homogeneous coordinates ["x" : "y" : "z"], where the coordinates ["x" : "y" : "z"] and ["tx" : "ty" : "tz"] are considered to represent the same point, for all nonzero values of "t". The points with coordinates ["x" : "y" : 1] are