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Essay / Crystal symmetry - 2463
Consider a regular polygon of n sides, a rotation by - around an axis normal to the plane of the polygon passing through its center is for it a symmetry operation. The cyclic group consists of n rotations and denoted Cn. The rotation groups consistent with the translational symmetry in the crystal are C1, C2, C3, C4 and C6. In this figure 3.1 which shows the projection of the atom on a plane is called stereographic projection. The point above the plane is denoted + and the point below the plane is denoted o. The nature of the rotation is defined by the center of the circle, i.e. a filled ellipse denotes a double axis, a filled triangle denotes a triple axis, a filled square denotes a quadruple axis and a filled hexagon denotes a sixfold axis of appropriate rotation. in the horizontal plane is denoted σh.σh shuttles with a rotation around the vertical axis. Figure 3.2 shows the horizontal reflection plane in the group of points.it denoted Chi.e. direct product of Cn with σh. The Cn group contains 2n