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A Euclidean graph (a graph embedded in some Euclidean space) is periodic if there exists a basis of that Euclidean space whose corresponding translations induce symmetries of that graph (i.e., application of any such translation to the graph embedded in the Euclidean space leaves the graph unchanged). Equivalently, a periodic Euclidean graph is ...
Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
In graph theory, a branch of mathematics, a periodic graph with respect to an operator F on graphs is one for which there exists an integer n > 0 such that F n (G) is isomorphic to G. [1] For example, every graph is periodic with respect to the complementation operator , whereas only complete graphs are periodic with respect to the operator ...
A Penrose tiling with rhombi exhibiting fivefold symmetry. A Penrose tiling is an example of an aperiodic tiling.Here, a tiling is a covering of the plane by non-overlapping polygons or other shapes, and a tiling is aperiodic if it does not contain arbitrarily large periodic regions or patches.
GeoGebra (a portmanteau of geometry and algebra) is an interactive geometry, algebra, statistics and calculus application, intended for learning and teaching mathematics and science from primary school to university level.
In geometry and crystallography, the Laves graph is an infinite and highly symmetric system of points and line segments in three-dimensional Euclidean space, forming a periodic graph. Three equal-length segments meet at 120° angles at each point, and all cycles use ten or more segments.
An aperiodic graph. The cycles in this graph have lengths 5 and 6; therefore, there is no k > 1 that divides all cycle lengths. A strongly connected graph with period three. In the mathematical area of graph theory, a directed graph is said to be aperiodic if there is no integer k > 1 that divides the length of every cycle of the graph.
In crystallography, a periodic graph or crystal net is a three-dimensional periodic graph, i.e., a three-dimensional Euclidean graph whose vertices or nodes are points in three-dimensional Euclidean space, and whose edges (or bonds or spacers) are line segments connecting pairs of vertices, periodic in three linearly independent axial directions.
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