  It is known that the space of convex polygons in the Euclidean plane with
fixed normals, up to homotheties and translations, endowed with the area form,
is isometric to a hyperbolic polyhedron. In this note we show a class of convex
polygons in the Lorentzian plane such that their moduli space, if the normals
are fixed and endowed with a suitable area, is isometric to a spherical
polyhedron. These polygons have an infinite number of vertices, are space-like,
contained in the future cone of the origin, and setwise invariant under the
action of a linear isometry.
