crystallographic group
1Non-Euclidean crystallographic group — In mathematics, a non Euclidean crystallographic group, NEC group or N.E.C. group is a discrete group of isometries of the hyperbolic plane. These symmetry groups correspond to the wallpaper groups in euclidean geometry. A NEC group which… …
2Crystallographic 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… …
3Crystallographic 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… …
4Crystallographic 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 …
5Crystallographic 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… …
6Space 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… …
7Wallpaper group — A wallpaper group (or plane symmetry group or plane crystallographic group) is a mathematical classification of a two dimensional repetitive pattern, based on the symmetries in the pattern. Such patterns occur frequently in architecture and… …
8Discrete group — Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product, direct sum semidirect product, wreath product …
9List of group theory topics — Contents 1 Structures and operations 2 Basic properties of groups 2.1 Group homomorphisms 3 Basic types of groups …
10Fuchsian group — In mathematics, a Fuchsian group is a particular type of group of isometries of the hyperbolic plane. A Fuchsian group is always a discrete group contained in the semisimple Lie group PSL(2,C). The name is given in honour of Immanuel Lazarus… …
