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
Plane partition Plane partition In mathematics and especially in combinatorics, a plane partition is a two-dimensional array of nonnegative integers formula_1 (with positive integer indices "i" and "j") that is nonincreasing in both indices. This means that Moreover only finitely many of the formula_4 are nonzero. A plane partitions may be represented visually by the placement of a stack of formula_1 unit cubes above the point ("i", "j") in the plane, giving a three-dimensional solid as shown in the picture. The "sum" of a plane partition is The sum describes the number of cubes of which the plane partition consists. The number