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  2. List of spherical symmetry groups - Wikipedia

    en.wikipedia.org/wiki/List_of_spherical_symmetry...

    There are five fundamental symmetry classes which have triangular fundamental domains: dihedral, cyclic, tetrahedral, octahedral, and icosahedral symmetry. This article lists the groups by Schoenflies notation , Coxeter notation , [ 1 ] orbifold notation , [ 2 ] and order.

  3. Molecular symmetry - Wikipedia

    en.wikipedia.org/wiki/Molecular_symmetry

    In chemistry, molecular symmetry describes the symmetry present in molecules and the classification of these molecules according to their symmetry. Molecular symmetry is a fundamental concept in chemistry, as it can be used to predict or explain many of a molecule's chemical properties , such as whether or not it has a dipole moment , as well ...

  4. Symmetry - Wikipedia

    en.wikipedia.org/wiki/Symmetry

    This article describes symmetry from three perspectives: in mathematics, including geometry, the most familiar type of symmetry for many people; in science and nature; and in the arts, covering architecture, art, and music. The opposite of symmetry is asymmetry, which refers to the absence of symmetry.

  5. Centrosymmetry - Wikipedia

    en.wikipedia.org/wiki/Centrosymmetry

    In crystallography, a centrosymmetric point group contains an inversion center as one of its symmetry elements. [1] In such a point group, for every point (x, y, z) in the unit cell there is an indistinguishable point (-x, -y, -z). Such point groups are also said to have inversion symmetry. [2] Point reflection is a similar term used in geometry.

  6. Molecular geometry - Wikipedia

    en.wikipedia.org/wiki/Molecular_geometry

    Geometries can also be computed by ab initio quantum chemistry methods to high accuracy. The molecular geometry can be different as a solid, in solution, and as a gas. The position of each atom is determined by the nature of the chemical bonds by which it is connected to its neighboring atoms.

  7. Crystal structure - Wikipedia

    en.wikipedia.org/wiki/Crystal_structure

    A crystal system is a set of point groups in which the point groups themselves and their corresponding space groups are assigned to a lattice system. Of the 32 point groups that exist in three dimensions, most are assigned to only one lattice system, in which case the crystal system and lattice system both have the same name.

  8. Symmetry of diatomic molecules - Wikipedia

    en.wikipedia.org/wiki/Symmetry_of_diatomic_molecules

    Molecular symmetry in physics and chemistry describes the symmetry present in molecules and the classification of molecules according to their symmetry. Molecular symmetry is a fundamental concept in the application of quantum mechanics in physics and chemistry, for example, it can be used to predict or explain many of a molecule's properties, such as its dipole moment and its allowed ...

  9. Symmetry element - Wikipedia

    en.wikipedia.org/wiki/Symmetry_element

    The elements of this symmetry group should not be confused with the "symmetry element" itself. Loosely, a symmetry element is the geometric set of fixed points of a symmetry operation. For example, for rotation about an axis, the points on the axis do not move and in a reflection the points that remain unchanged make up a plane of symmetry.