n-fold rotation
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Detachment fold — A detachment fold occurs as layer parallel thrusting along a detachment fault develops without upward propagation of a fault; the accommodation of the strain produced by thrusting results in the folding of the overlying rock units. As a visual… … Wikipedia
Improper rotation — In 3D geometry, an improper rotation, also called rotoreflection or rotary reflection is, depending on context, a linear transformation or affine transformation which is the combination of a rotation about an axis and an inversion about the… … 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
Rotational symmetry — Generally speaking, an object with rotational symmetry is an object that looks the same after a certain amount of rotation. An object may have more than one rotational symmetry; for instance, if reflections or turning it over are not counted, the … 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
Wallpaper 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… … Wikipedia
Symmetry combinations — This article discusses various symmetry combinations.In 2D, mirror image symmetry in combination with n fold rotational symmetry, with the center of rotational symmetry on the line of symmetry, implies mirror image symmetry with respect to lines… … Wikipedia
Tetrahedral symmetry — A regular tetrahedron has 12 rotational (or orientation preserving) symmetries, and a total of 24 symmetries including transformations that combine a reflection and a rotation.The group of symmetries that includes reflections is isomorphic to S 4 … Wikipedia
Screw axis — The screw axis (helical axis or twist axis) of an object is a parameter for describing simultaneous rotation and translation components of that object.The axis is a directed line in space, along which a translation may occur, and about which… … Wikipedia
Schoenflies notation — The Schoenflies notation is one of two conventions commonly used to describe crystallographic point groups. This notation is used in spectroscopy. The other convention is the Hermann Mauguin notation, also known as the International notation. A… … Wikipedia
Euclidean group — In mathematics, the Euclidean group E ( n ), sometimes called ISO( n ) or similar, is the symmetry group of n dimensional Euclidean space. Its elements, the isometries associated with the Euclidean metric, are called Euclidean moves.These groups… … Wikipedia
