crystallographic point group

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• Crystallographic point group — 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… …   Wikipedia

• Point group — The Bauhinia blakeana flower on the Hong Kong flag has C5 symmetry; the star on each petal has D5 symmetry. In geometry, a point group is a group of geometric symmetries (isometries) that keep at least one point fixed. Point groups can exist in a …   Wikipedia

• Point groups in three dimensions — In geometry, a point group in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry group of a sphere. It is a subgroup of the orthogonal group O(3), the group of all isometries… …   Wikipedia

• Crystallographic restriction theorem — The crystallographic restriction theorem in its basic form was based on the observation that the rotational symmetries of a crystal are usually limited to 2 fold, 3 fold, 4 fold, and 6 fold. However, quasicrystals can occur with other symmetries …   Wikipedia

• Crystallographic database — A crystallographic database is a database specifically designed to store information about crystals and crystal structures. Crystals are solids having, in all three dimensions of space, a regularly repeating arrangement of atoms, ions, or… …   Wikipedia

• Point groups in two dimensions — In geometry, a point group in two dimensions is an isometry group in two dimensions that leaves the origin fixed, or correspondingly, an isometry group of a circle. It is a subgroup of the orthogonal group O(2), the group of all isometries which… …   Wikipedia

• Crystallographic image processing — (CIP) is a set of methods for determining the atomic structure of crystalline matter from high resolution electron microscopy (HREM) images obtained in a transmission electron microscope (TEM). The term was created in the research group of Sven… …   Wikipedia

• Discrete group — Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product, direct sum semidirect product, wreath product …   Wikipedia

• List of group theory topics — Contents 1 Structures and operations 2 Basic properties of groups 2.1 Group homomorphisms 3 Basic types of groups …   Wikipedia

• List of the 230 crystallographic 3D space groups — Triclinic system = Note. An e plane is a double glide plane, one having glides in two different directions. They are found in five space groups, all in the orthorhombic system and with a centered lattice. The use of the symbol e became official… …   Wikipedia

• Space group — In mathematics and geometry, a space group is a symmetry group, usually for three dimensions, that divides space into discrete repeatable domains. In three dimensions, there are 219 unique types, or counted as 230 if chiral copies are considered… …   Wikipedia