1-Dimensional Orbits in Flat Projective Planes.
We study 2-frieze patterns generalizing that of the classical Coxeter-Conway frieze patterns. The geometric realization of this space is the space of -gons (in the projective plane and in 3-dimensional vector space) which is a close relative of the moduli space of genus curves with marked points. We show that the space of 2-frieze patterns is a cluster manifold and study its algebraic and arithmetic properties.