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
Three-dimensional space line or are parallel (do not meet). Three distinct planes, no pair of which are parallel, can either meet in a common line, meet in a unique common point or have no point in common. In the last case, the three lines of intersection of each pair of planes are mutually parallel. A line can lie in a given plane, intersect that plane in a unique point or be parallel to the plane. In the last case, there will be lines in the plane that are parallel to the given line. A hyperplane is a subspace of one dimension less