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Symmetric graph. The Petersen graph is a (cubic) symmetric graph. Any pair of adjacent vertices can be mapped to another by an automorphism, since any five-vertex ring can be mapped to any other. In the mathematical field of graph theory, a graph G is symmetric (or arc-transitive) if, given any two pairs of adjacent vertices u1—v1 and u2—v2 ...
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 ...
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 ...
Asymmetry. Asymmetry is the absence of, or a violation of, symmetry (the property of an object being invariant to a transformation, such as reflection). [1] Symmetry is an important property of both physical and abstract systems and it may be displayed in precise terms or in more aesthetic terms. [2]
In group theory, the symmetry group of a geometric object is the group of all transformations under which the object is invariant, endowed with the group operation of composition. Such a transformation is an invertible mapping of the ambient space which takes the object to itself, and which preserves all the relevant structure of the object.
Symmetry occurs not only in geometry, but also in other branches of mathematics. Symmetry is a type of invariance: the property that a mathematical object remains unchanged under a set of operations or transformations. [1] Given a structured object X of any sort, a symmetry is a mapping of the object onto itself which preserves the structure.
Crystal structure of table salt (sodium in purple, chlorine in green) In crystallography, crystal structure is a description of ordered arrangement of atoms, ions, or molecules in a crystalline material. [1] Ordered structures occur from intrinsic nature of constituent particles to form symmetric patterns that repeat along the principal ...
Similarly, if the exponent of y is always even in the equation of the curve then the x-axis is an axis of symmetry for the curve. If the sum of the degrees of x and y in each term is always even or always odd, then the curve is symmetric about the origin and the origin is called a center of the curve. Determine any bounds on the values of x and y.