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Rotational symmetry of order n, also called n-fold rotational symmetry, or discrete rotational symmetry of the n th order, with respect to a particular point (in 2D) or axis (in 3D) means that rotation by an angle of (180°, 120°, 90°, 72°, 60°, 51 3 ⁄ 7 °, etc.) does not change the object. A "1-fold" symmetry is no symmetry (all ...
Their symmetry group has two elements, the identity and a diagonal reflection. Z can be oriented in 4 ways: 2 by rotation, and 2 more for the mirror image. It has point symmetry, also known as rotational symmetry of order 2. Its symmetry group has two elements, the identity and the 180° rotation. I can be oriented in 2 ways by rotation.
The twelve rotations form the rotation (symmetry) group of the figure. In group theory , the symmetry group of a geometric object is the group of all transformations under which the object is invariant , endowed with the group operation of composition .
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The tetrahedral group of order 12, rotational symmetry group of the regular tetrahedron. It is isomorphic to A 4. The conjugacy classes of T are: identity; 4 × rotation by 120°, order 3, cw; 4 × rotation by 120°, order 3, ccw; 3 × rotation by 180°, order 2; The octahedral group of order 24, rotational symmetry group of the cube and the ...
For any symmetry group containing a glide reflection, the glide vector is one half of an element of the translation group. If the translation vector of a glide plane operation is itself an element of the translation group, then the corresponding glide plane symmetry reduces to a combination of reflection symmetry and translational symmetry.
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