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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]
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The eight vertices on the 3-fold symmetry axes can be seen as the vertices of a fifth cube of the same size. [3] Referring to the images below, the four old cubes are called colored, and the new one black. Each colored cube has two opposite vertices on a 3-fold symmetry axis, which are shared with the black cube.
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.
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 ...
A high-index reflective subgroup is the prismatic octahedral symmetry, [4,3,2] (), order 96, subgroup index 4, (Du Val #44 (O/C 2;O/C 2) *, Conway ± 1 / 24 [O×O].2). The truncated cubic prism has this symmetry with Coxeter diagram and the cubic prism is a lower symmetry construction of the tesseract, as .
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 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 .
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