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In crystallography, a crystallographic point group is a three dimensional point group whose symmetry operations are compatible with a three dimensional crystallographic lattice. According to the crystallographic restriction it may only contain one-, two-, three-, four- and sixfold rotations or rotoinversions. This reduces the number of ...
The (finite) list of all symmetry operations which leave the given point invariant taken together make up another group, which is known as the site symmetry group of that point. [4] By definition, all points with the same site symmetry group, or a conjugate site symmetry group, are assigned the same Wyckoff position.
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 crystallographic point groups that exist in three dimensions, most are assigned to only one lattice system, in which case both the crystal and lattice systems have the same name. However ...
The full and short symbols for all 32 crystallographic point groups are given in crystallographic point groups page. Besides five cubic groups, there are two more non-crystallographic icosahedral groups (I and I h in Schoenflies notation) and two limit groups (K and K h in Schoenflies notation). The Hermann–Mauguin symbols were not designed ...
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.
The 27 point groups in the table plus T, T d, T h, O and O h constitute 32 crystallographic point groups. Groups with n = ∞ are called limit groups or Curie groups . There are two more limit groups, not listed in the table: K (for Kugel , German for ball, sphere), the group of all rotations in 3-dimensional space; and K h , the group of all ...
These groups are characterized by an n-fold improper rotation axis S n, where n is necessarily even. The S 2 group is the same as the C i group in the nonaxial groups section. S n groups with an odd value of n are identical to C nh groups of same n and are therefore not considered here (in particular, S 1 is identical to C s).
The 54 hemisymmorphic space groups contain only axial combination of symmetry elements from the corresponding point groups. Example for point group 4/mmm (): hemisymmorphic space groups contain the axial combination 422, but at least one mirror plane m will be substituted with glide plane, for example P4/mcc (, 35h), P4/nbm (, 36h), P4/nnc ...