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Fundamental domain
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== Examples == Examples in the three-dimensional Euclidean space '''R'''<sup>3</sup>. *for ''n''-fold rotation: an orbit is either a set of ''n'' points around the axis, or a single point on the axis; the fundamental domain is a sector *for reflection in a plane: an orbit is either a set of 2 points, one on each side of the plane, or a single point in the plane; the fundamental domain is a half-space bounded by that plane *for reflection in a point: an orbit is a set of 2 points, one on each side of the center, except for one orbit, consisting of the center only; the fundamental domain is a half-space bounded by any plane through the center *for 180Β° rotation about a line: an orbit is either a set of 2 points opposite to each other with respect to the axis, or a single point on the axis; the fundamental domain is a half-space bounded by any plane through the line *for discrete [[translational symmetry]] in one direction: the orbits are translates of a 1D lattice in the direction of the translation vector; the fundamental domain is an infinite slab *for discrete translational symmetry in two directions: the orbits are translates of a 2D lattice in the plane through the translation vectors; the fundamental domain is an infinite bar with [[parallelogram]]matic cross section *for discrete translational symmetry in three directions: the orbits are translates of the lattice; the fundamental domain is a [[primitive cell]] which is e.g. a [[parallelepiped]], or a [[Wigner-Seitz cell]], also called [[Voronoi diagram|Voronoi cell]]/diagram. In the case of translational symmetry combined with other symmetries, the fundamental domain is part of the primitive cell. For example, for [[wallpaper group]]s the fundamental domain is a factor 1, 2, 3, 4, 6, 8, or 12 smaller than the primitive cell.
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