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
Cayley plane Cayley plane In mathematics, the Cayley plane (or octonionic projective plane) P(O) is a projective plane over the octonions. It was discovered in 1933 by Ruth Moufang, and is named after Arthur Cayley (for his 1845 paper describing the octonions). More precisely, there are two objects called Cayley planes, namely the real and the complex Cayley plane. The real Cayley plane is the symmetric space F/Spin(9), where F is a compact form of an exceptional Lie group and Spin(9) is the spin group of nine-dimensional Euclidean space (realized in F). It admits a cell decomposition into three cells, of dimensions