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
The Hero with a Thousand Faces sometimes assisted by "allies". As the hero faces the "ordeal," he encounters the greatest challenge of the journey. Upon rising to the challenge, the hero will receive a reward, or "boon". Campbell's theory of the monomyth continues with the inclusion of a metaphorical "death" and "resurrection". The hero must then decide to return with this "boon" to the "ordinary world". The hero then faces more trials on "the road back". Upon the hero's return, the boon or gift may be used to improve the hero's ordinary world, in what Campbell calls, the "application of the boon". While many myths do