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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]
Rotational symmetry of order n, also called n-fold rotational symmetry, or discrete rotational symmetry of the n th order, with respect to a particular point (in 2D) or axis (in 3D) means that rotation by an angle of (180°, 120°, 90°, 72°, 60°, 51 3 ⁄ 7 °, etc.) does not change the object. A "1-fold" symmetry is no symmetry (all ...
The two groups are obtained from it by changing 2-fold rotational symmetry to 4-fold, and adding 5-fold symmetry, respectively. There are two crystallographic point groups with the property that no crystallographic point group has it as proper subgroup: O h and D 6h. Their maximal common subgroups, depending on orientation, are D 3d and D 2h.
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 .
The compound of four cubes or Bakos compound [1] is a face-transitive polyhedron compound of four cubes with octahedral symmetry. It is the dual of the compound of four octahedra. Its surface area is 687/77 square lengths of the edge. [2] Its Cartesian coordinates are (±3, ±3, ±3) and the permutations of (±5, ±1, ±1).
The 16-cell edges projected onto a 3-sphere represent 6 great circles of B4 symmetry. 3 circles meet at each vertex. 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.
Vergence is used to provide an overall characterization, in the symmetry (or asymmetry) of folds, and can be used to observe changes in small-scale structures in relation to the axis of a large fold. [3] The vergence of a fold lies parallel to the surrounding surfaces of a fold, so if these surrounding surfaces are not horizontal, the vergence ...
These axes are arranged as 3-fold axes in a cube, directed along its four space diagonals (the cube has 4 / m 3 2 / m symmetry). These symbols are constructed the following way: First position – symmetrically equivalent directions of the coordinate axes x, y, and z. They are equivalent due to the presence of diagonal 3-fold ...