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A hyperbolic plane O H of positive curvature can be realized on the exterior domain with respect to an oval curve in a projective plane. The plane O H is the Cayley – Klein model of a two-dimensional de Sitter space. It is proved that there is no regular mosaic on the plane O H . 2010 Mathematics Subject Classification: 51M10; 51M20; 52C20

To a question on the existence of regular mosaics on a hyperbolic plane of positive curvature