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In structural geology, a fold is a stack of originally planar surfaces, such as sedimentary strata, that are bent or curved ("folded") during permanent deformation. Folds in rocks vary in size from microscopic crinkles to mountain-sized folds. They occur as single isolated folds or in periodic sets (known as fold trains).
Each circle represents axes of 4-fold symmetry. The 24-cell edges projected onto a 3-sphere represent the 16 great circles of F4 symmetry. Four circles meet at each vertex. Each circle represents axes of 3-fold symmetry. The 600-cell edges projected onto a 3-sphere represent 72 great circles of H4 symmetry. Six circles meet at each vertex.
C i (equivalent to S 2) – inversion symmetry; C 2 – 2-fold rotational symmetry; C s (equivalent to C 1h and C 1v) – reflection symmetry, also called bilateral symmetry. Patterns on a cylindrical band illustrating the case n = 6 for each of the 7 infinite families of point groups. The symmetry group of each pattern is the indicated group.
There are five fundamental symmetry classes which have triangular fundamental domains: dihedral, cyclic, tetrahedral, octahedral, and icosahedral symmetry. This article lists the groups by Schoenflies notation , Coxeter notation , [ 1 ] orbifold notation , [ 2 ] and order.
Therefore, the number of 2-, 3-, 4-, and 6-fold rotocenters per primitive cell is 4, 3, 2, and 1, respectively, again including 4-fold as a special case of 2-fold, etc. 3-fold rotational symmetry at one point and 2-fold at another one (or ditto in 3D with respect to parallel axes) implies rotation group p6, i.e. double translational symmetry ...
The vergence of a fold can help a geologist determine several characteristics of folding on a larger scale, including the style, position, and geometry of the folding. [ 3 ] By observing vergence in a fold, geologists can record data that can be used to calculate the approximate position and geometry of a larger area, and therefore assist ...
In geology, 3D fold evolution is the study of the full three dimensional structure of a fold as it changes in time. A fold is a common three-dimensional geological structure that is associated with strain deformation under stress .
In geometry, a point group is a mathematical group of symmetry operations (isometries in a Euclidean space) that have a fixed point in common. The coordinate origin of the Euclidean space is conventionally taken to be a fixed point, and every point group in dimension d is then a subgroup of the orthogonal group O(d).