On the geodesic trapezoid of constant width in a plane of constant curvature

A series of convex bodies of constant width are constructed from a geodesic quadrilateral in the 2-dimensional unit sphere and hyperbolic plane, which continuously vary from the geodesic disc to the Reuleaux triangle. The Blaschke-Lebesgue theorem for them is proved. For a spherical convex body of constant width, we prove that its polar is also a spherical convex body of constant width and the Blaschke-Santaló type inequality.