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across a specific fixed point. When dealing with crystal structures and in the physical sciences the terms inversion symmetry, inversion center or centrosymmetric...

molecular symmetry describes the symmetry present in molecules and the classification of these molecules according to their symmetry. Molecular symmetry is a...

for vector fields the symmetry group can also be E +(m). For symmetry with respect to rotations about a point we can take that point as origin. These rotations...

orientation-reversing symmetries, so that its proper symmetry group is equal to its full symmetry group. Any symmetry group whose elements have a common fixed point, which...

Lie point symmetry is a concept in advanced mathematics. Towards the end of the nineteenth century, Sophus Lie introduced the notion of Lie group in order...

Symmetry (from Ancient Greek συμμετρία (summetría) 'agreement in dimensions, due proportion, arrangement') in everyday life refers to a sense of harmonious...

emission spectrum and the only known PPN with point-reflection-symmetric deviations from axial symmetry. The Frosty Leo Nebula has two lobes that are...

right-handed coordinate system, symmetry under a point reflection is also called a left-right symmetry. Rotational symmetry is symmetry with respect to some or...

Finite spherical symmetry groups are also called point groups in three dimensions. There are five fundamental symmetry classes which have triangular fundamental...

Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state spontaneously ends up in an...

same point symmetry as the underlying Bravais lattice. For example, the cube, truncated octahedron, and rhombic dodecahedron have point symmetry Oh, since...

pattern is unit cell of the structure. The unit cell completely reflects symmetry and structure of the entire crystal, which is built up by repetitive translation...

crystallography, a symmetry element is a point, line, or plane about which symmetry operations can take place. In particular, a symmetry element can be a...

In crystallography, a crystallographic point group is a three dimensional point group whose symmetry operations are compatible with a three dimensional...

space group is the symmetry group of a repeating pattern in space, usually in three dimensions. The elements of a space group (its symmetry operations) are...

transformations). Since each face has point symmetry, a parallelepiped is a zonohedron. Also the whole parallelepiped has point symmetry Ci (see also triclinic). Each...

a point reflection of a sphere through its center are all symmetry operations. Each symmetry operation is performed with respect to some symmetry element...

symmetry) are discrete point symmetries (or equivalently, symmetries on the sphere). They are among the crystallographic point groups of the cubic crystal...

symmetry for each permutation of the four diagonals of the cube. Chiral and full (or achiral) octahedral symmetry are the discrete point symmetries (or...

chiral icosahedral symmetry of chiral objects and full icosahedral symmetry or achiral icosahedral symmetry are the discrete point symmetries (or equivalently...