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A fold axis "is the closest approximation to a straight line that when moved parallel to itself, generates the form of the fold". [2] (Ramsay 1967). A fold that can be generated by a fold axis is called a cylindrical fold. This term has been broadened to include near-cylindrical folds. Often, the fold axis is the same as the hinge line. [3] [4]
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 ...
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.
In 2016 it could be shown by Bernhard Klaassen that every discrete rotational symmetry type can be represented by a monohedral pentagonal tiling from the same class of pentagons. [15] Examples for 5-fold and 7-fold symmetry are shown below. Such tilings are possible for any type of n-fold rotational symmetry with n>2.
Free to use software to digitize geological cross-sections, and display and edit borehole logs Geoscience ANALYST [30] Free 3D visualization and communication software for integrated, multi-disciplinary geoscience and mining data and models, which also connects to Python through geoh5py, its open-source API Mira Geoscience Ltd. Free / Proprietary
In his original use of the term, however, he did, in fact, use the up-dip direction of the fold. The main reason this creates confusion is a result of the common definition of fold-facing in geology, which is described as the direction (normal to the axis of a fold and corresponding to the axial plane) that points towards younger beds.
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The symmetry group of the diagram is the symmetric group S 3 which acts by permuting the three legs. This gives rise to an S 3 group of outer automorphisms of Spin(8). This automorphism group permutes the three 8-dimensional irreducible representations of Spin(8); these being the vector representation and two chiral spin representations.