This Demonstration shows Möbius triangles on a sphere. Möbius triangles are congruent spherical triangles that completely cover a sphere without overlap. The angles of these triangles are , , and , where , , and are in the set . Such a Möbius triangle is denoted by . There is an infinite family of dihedral Möbius triangles, and three triangles , , and that correspond to the tetrahedral, octahedral, and icosahedral symmetry groups, respectively.