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The (finite) list of all symmetry operations which leave the given point invariant taken together make up another group, which is known as the site symmetry group of that point. [4] By definition, all points with the same site symmetry group, or a conjugate site symmetry group, are assigned the same Wyckoff position.
In geometry, an arrangement of lines is the subdivision of the Euclidean plane formed by a finite set of lines. An arrangement consists of bounded and unbounded convex polygons, the cells of the arrangement, line segments and rays, the edges of the arrangement, and points where two or more lines cross, the vertices of the arrangement.
In linear algebra, linear transformations can be represented by matrices.If is a linear transformation mapping to and is a column vector with entries, then there exists an matrix , called the transformation matrix of , [1] such that: = Note that has rows and columns, whereas the transformation is from to .
In invariant theory, the representation theory of the symmetric group on two points is quite simple and is seen as writing a function of two variables as a sum of its symmetric and anti-symmetric parts: Setting f s (x, y) = f(x, y) + f(y, x), and f a (x, y) = f(x, y) − f(y, x), one gets that 2⋅f = f s + f a. This process is known as ...
Cascading is syntactic sugar that eliminates the need to list the object repeatedly. This is particularly used in fluent interfaces , which feature many method calls on a single object. This is particularly useful if the object is the value of a lengthy expression, as it eliminates the need to either list the expression repeatedly or use a ...
Configurations (4 3 6 2) (a complete quadrangle, at left) and (6 2 4 3) (a complete quadrilateral, at right).. In mathematics, specifically projective geometry, a configuration in the plane consists of a finite set of points, and a finite arrangement of lines, such that each point is incident to the same number of lines and each line is incident to the same number of points.
A drop-down list or drop-down menu or drop menu, with generic entries. A drop-down list (DDL), drop-down menu or just drop-down [1] – also known as a drop menu, pull-down list, picklist – is a graphical control element, similar to a list box, that allows the user to choose one value from a list either by clicking or hovering over the menu ...
Animation of a half-turn ambigram of the word ambigram, with 180-degree rotational symmetry [1]. An ambigram is a calligraphic composition of glyphs (letters, numbers, symbols or other shapes) that can yield different meanings depending on the orientation of observation.
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