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
Plane of rotation geometric algebra, with the planes of rotations associated with simple bivectors in the algebra. For this article, all "planes" are planes through the origin, that is they contain the zero vector. Such a plane in -dimensional space is a two-dimensional linear subspace of the space. It is completely specified by any two non-zero and non-parallel vectors that lie in the plane, that is by any two vectors and , such that where is the exterior product from exterior algebra or geometric algebra (in three dimensions the cross product can be used). More precisely, the quantity is the bivector associated with