The closed cyclic self-intersecting hexagon formed by joining the adjacent antiparallels in the construction of the cosine circle. The sides of this hexagon have the property that, in addition to P_1 Q_2, P_2 Q_3, and P_3 Q_1 being antiparallel to A_1 A_2, A_2 A_3, A_1 A_3, the remaining sides P_1 Q_1 ∥A_2 A_3, P_2 Q_2 ∥A_1 A_3, and P_3 Q_3 ∥A_1 A_2. The cosine hexagon is a special case of a Tucker hexagon.

cosine circle | Lemoine hexagon | Tucker hexagon