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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 ...
However, there are three more infinite series of symmetry groups with this abstract group type: C nv of order 2n, the symmetry group of a regular n-sided pyramid; D nd of order 4n, the symmetry group of a regular n-sided antiprism; D nh of order 4n for odd n. For n = 1 we get D 2, already covered above, so n ≥ 3. Note the following property:
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. Such a transformation is an invertible mapping of the ambient space which takes the object to itself, and which preserves all the relevant structure of the object.
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 ...
In chemistry, octahedral molecular geometry, also called square bipyramidal, [1] describes the shape of compounds with six atoms or groups of atoms or ligands symmetrically arranged around a central atom, defining the vertices of an octahedron. The octahedron has eight faces, hence the prefix octa.
Finite spherical symmetry groups are also called point groups in three dimensions. 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.
The crystallographic point group or crystal class is the mathematical group comprising the symmetry operations that leave at least one point unmoved and that leave the appearance of the crystal structure unchanged. These symmetry operations include
In geometry and crystallography, a Bravais lattice is a category of translative symmetry groups (also known as lattices) in three directions. Such symmetry groups consist of translations by vectors of the form R = n 1 a 1 + n 2 a 2 + n 3 a 3, where n 1, n 2, and n 3 are integers and a 1, a 2, and a 3 are three non-coplanar vectors, called ...