Point groups in three dimensions the finite subgroups of SO(3), are: the cyclic groups "C" (the rotation group of a canonical pyramid), the dihedral groups "D" (the rotation group of a uniform prism, or canonical bipyramid), and the rotation groups "T", "O" and "I" of a regular tetrahedron, octahedron/cube and icosahedron/dodecahedron. In particular, the dihedral groups "D", "D" etc. are the rotation groups of plane regular polygons embedded in three-dimensional space, and such a figure may be considered as a degenerate regular prism. Therefore, it is also called a "dihedron" (Greek: solid with two faces), which explains the name "dihedral group". The rotation group of
Möbius plane 5 faces correspond to concyclical quadruples than the sixth quadruple of points is concyclical, too. The converse is true, too. Theorem (Chen): Only a Möbius plane formula_118 satisfies the Theorem of Miquel. Because of the last Theorem a Möbius plane formula_122 is called a "miquelian Möbius plane". Remark: The "minimal model" of a Möbius plane is miquelian. It is isomorphic to the Möbius plane Remark: If we choose formula_129 the field of complex numbers, there is "no suitable" quadratic form at all. Remark: A stereographic projection shows: formula_122 is isomorphic to the geometry of the plane Remark: A proof of