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 chess travel-size board are included on Meder's website. There is software for playing Tri-D Chess. "Parmen" is a Windows application written by Doug Keenan and available free on his website. A free Android version of Tri D Chess is offered by AwfSoft. As well as in "Star Trek", multi-dimensional chess games are featured in various fictional works, usually in a futuristic or science fiction setting. Examples include "Blake's 7," "UFO," "Starman Jones," "Unreal 2," the Legion of Super-Heroes, "Doctor Who," and "The Lego Movie." The concept is parodied in "Futurama" as tridimensional "Scrabble". Bibliography Raumschach "Star Trek" Tri-D Three-dimensional chess Three-dimensional