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 has three dimensions because the length of a box is independent of its width or breadth. In the technical language of linear algebra, space is three-dimensional because every point in space can be described by a linear combination of three independent vectors. A vector can be pictured as an arrow. The vector's magnitude is its length, and its direction is the direction the arrow points. A vector in can be represented by an ordered triple of real numbers. These numbers are called the components of the vector. The dot product of two vectors and is defined as: The magnitude of