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 is the surface integral over the boundary of the volume . The closed manifold is quite generally the boundary of oriented by outward-pointing normals, and is the outward pointing unit normal field of the boundary . ( may be used as a shorthand for .) Three-dimensional space has a number of topological properties that distinguish it from spaces of other dimension numbers. For example, at least three dimensions are required to tie a knot in a piece of string. With the space formula_21, the topologists locally model all other 3-manifolds. Three-dimensional space Three-dimensional space (also: 3-space or, rarely, tri-dimensional space)