crystallographic point group

They are among the crystallographic point groups of the cubic crystal system.

The remaining seven are, with bolding of the 5 crystallographic point groups (see also above):

The complete set of 32 crystallographic point groups was published in 1936 by Rosenthal and Murphy.

Thus we have, with bolding of the 2 cyclic crystallographic point groups:

There are a total of 32 crystallographic point groups, 30 of which are relevant to chemistry.

However, the 32 classes of crystal symmetry are one-and-the-same as the 32 crystallographic point groups.

There are thus 10 two-dimensional crystallographic point groups:

A crystallographic point group is a point group which will work with translational symmetry in three dimensions.

The 7 crystal systems consist of 32 crystal classes (corresponding to the 32 crystallographic point groups) as shown in the following table.

An abbreviated form of the Hermann-Mauguin notation commonly used for space groups also serves to describe crystallographic point groups.

The characteristic rotation and mirror symmetries of the group of atoms, or unit cell, is described by its crystallographic point group.

Icosahedral symmetry is not compatible with translational symmetry, so there are no associated crystallographic point groups or space groups.

However, the crystallographic restriction of the infinite families of general point groups results in there being only 32 crystallographic point groups.

In mathematics, a rod group is a three-dimensional line group whose point group is one of the axial crystallographic point groups.

The full and short symbols for all 32 crystallographic point groups are given in crystallographic point groups page.

In terms of its crystallographic point group, the symmetry of triphenylene is classified as D in Schoenflies notation.

Combinations of operations of the crystallographic point groups with the addition symmetry operations produce the 230 crystallographic space groups.

The symmetry group at each lattice point is an axial crystallographic point group with the main axis being perpendicular to the lattice plane.

If the point group is constrained to be a crystallographic point group, a symmetry of some three-dimensional lattice, then the resulting line group is called a rod group.

The program POINT lists character tables of crystallographic point groups, Kronecker multiplication tables of their irreducible representations and further useful symmetry information.

The space groups in three dimensions are made from combinations of the 32 crystallographic point groups with the 14 Bravais lattices, each of the latter belonging to one of 7 lattice systems.

In particular cases, however, when the ions reside on lattice site of certain crystallographic point groups, the inclusion of higher order moments, i.e. multipole moments of the charge density might be required.

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.

In crystallography, a crystallographic point group is a set of symmetry operations, like rotations or reflections, that leave a central point fixed while moving other directions and faces of the crystal to the positions of features of the same kind.

There are two crystallographic point groups with the property that no crystallographic point group has it as proper subgroup: O and D. Their maximal common subgroups, depending on orientation, are D and D.