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  1. A parallelogram has two-fold rotational symmetry around its center. We will denote the two-fold axis with a vertical “pointy” ellipse (Fig. 2, left) and with the number 2.

  2. What is a symmetry? Roughly speaking, a symmetry is a property of some object which remains invariant under some operations. Note that the notion of symmetry requires both an object, and the operation which acts or operates on the object. Invariance means that the property of the

  3. higher than 2 (i.e., 3, 4 and 6) define the primary symmetry direction and always come upfront in the point-group symbol, and right after the lattice symbol (P , I, F , etc.) in the space group symbols. This is the meaning of the first character in the symbol 6mm.

  4. Symmetries in Physics Chapter 1 ETH Zurich, HS15 Prof. N. Beisert 04.10.2015 1 Two-Dimensional Rotations Symmetries in physics are typically expressed by mathematical groups acting in some speci c way on some objects or spaces. In the rst chapter we introduce the basic notions of group theory using the example of rotations in two spatial ...

  5. Rotation symmetries. An equilateral triangle can be rotated by 120 , 240 , or 360 angles without really changing it. If you were to close your eyes, and a friend rotated the triangle by one of those angles, then after opening your eyes you would not notice that anything had changed.

  6. A shape with rotation (or rotational) symmetry can be rotated round its centre so that it fits on top of itself more than one way. The order of rotation symmetry is the number of different positions a shape fits on top of itself. We say that a shape with no rotation symmetry has order 1. as it fits on top of itself in only one way.

  7. A shape has rotational symmetry when it coincides with itself after a rotation of less than 360 o about its centre. Order of Rotation is the number of times a shape coinsides with itself

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