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
Projective plane (see below). A permutation of the seven points that carries collinear points (points on the same line) to collinear points is called a "collineation" or "symmetry" of the plane. The collineations of a geometry form a group under composition, and for the Fano plane this group (PΓL(3,2) = PGL(3,2)) has 168 elements. The theorem of Desargues is universally valid in a projective plane if and only if the plane can be constructed from a three-dimensional vector space over a skewfield as above. These planes are called Desarguesian planes, named after Girard Desargues. The real (or complex) projective plane and the