Аннотация:A hyperbolic plane H of positive curvature can be realized on the ideal domain of a Lobachevskii plane. The plane H is the projective Cayley-Klein model of a two-dimensional de Sitter space. It is shown that on H there are no finite regular polygons topologically equivalent to a disk. A finite equiangular polygon homeomorphic to a disk is a quadrangle with hyperbolic quasiangles. In the plane H we study also equiangular and regular polygons homeomorphic to the Möbius band. It is proved that the interior angle at the vertex of a finite equiangular Möbius polygon of the plane H is a non-convex elliptic pseudoangle.