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
Benz plane the classical Minkowski plane. Analogously to the classical Möbius and Laguerre planes, there exists a 3-dimensional model: The classical Minkowski plane is isomorphic to the geometry of plane sections of a hyperboloid of one sheet (non degenerated quadric of index 2) in 3-dimensional projective space. Similar to the first two cases we get the (axiomatic) Minkowski plane. Because of the essential role of the circle (considered as the non-degenerate conic in a projective plane) and the plane description of the original models the three types of geometries are subsumed to planar circle geometries or in honor of Walter Benz, who