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A wallpaper group (or plane symmetry group or plane crystallographic group) is a mathematical classification of a two-dimensional repetitive pattern, based on the symmetries in the pattern. Such patterns occur frequently in architecture and decorative art, especially in textiles, tiles, and wallpaper. The simplest wallpaper group, Group p 1 ...
A geometric shape or object is symmetric if it can be divided into two or more identical pieces that are arranged in an organized fashion. [5] This means that an object is symmetric if there is a transformation that moves individual pieces of the object, but doesn't change the overall shape. The type of symmetry is determined by the way the ...
Herringbone pattern. The herringbone pattern is an arrangement of rectangles used for floor tilings and road pavement, so named for a fancied resemblance to the bones of a fish such as a herring. The blocks can be rectangles or parallelograms. The block edge length ratios are usually 2:1, and sometimes 3:1, but need not be even ratios.
The group of isometries of space induces a group action on objects in it, and the symmetry group Sym (X) consists of those isometries which map X to itself (as well as mapping any further pattern to itself). We say X is invariant under such a mapping, and the mapping is a symmetry of X. The above is sometimes called the full symmetry group of X ...
A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called tiles, with no overlaps and no gaps. In mathematics, tessellation can be generalized to higher dimensions and a variety of geometries. A periodic tiling has a repeating pattern. Some special kinds include regular tilings with regular ...
e. Edge detection includes a variety of mathematical methods that aim at identifying edges, defined as curves in a digital image at which the image brightness changes sharply or, more formally, has discontinuities. The same problem of finding discontinuities in one-dimensional signals is known as step detection and the problem of finding signal ...
The symmetry groups are named here by three naming schemes: International notation, orbifold notation, and Coxeter notation. There are three kinds of symmetry groups of the plane: 2 families of rosette groups – 2D point groups. 7 frieze groups – 2D line groups. 17 wallpaper groups – 2D space groups.
Symmetry (geometry) A drawing of a butterfly with bilateral symmetry, with left and right sides as mirror images of each other. In geometry, an object has symmetry if there is an operation or transformation (such as translation, scaling, rotation or reflection) that maps the figure/object onto itself (i.e., the object has an invariance under ...