منابع مشابه
Folding Equilateral Plane Graphs
We consider two types of folding applied to equilateral plane graph linkages. First, under continuous folding motions, we show how to reconfigure any linear equilateral tree (lying on a line) into a canonical configuration. By contrast, such reconfiguration is known to be impossible for linear (nonequilateral) trees and for (nonlinear) equilateral trees. Second, under instantaneous folding moti...
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We consider L-graphs, that is contact graphs of axis-aligned L-shapes in the plane, all with the same rotation. We provide several characterizations of Lgraphs, drawing connections to Schnyder realizers and canonical orders of maximally planar graphs. We show that every contact system of L’s can always be converted to an equivalent one with equilateral L’s. This can be used to show a stronger v...
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It is shown that an equilateral convex pentagon tiles the plane if and only if it has two angles adding to 180 o or it is the unique equilateral convex pentagon with Although the area of mathematical tilings has been of interest for a long time there is still much to be discovered. We do not even know which convex polygons tile the plane. Furthermore, for those polygons which do tile, new tilin...
متن کاملEquilateral Quantum Graphs and Their Decorations
We consider magnetic Schrödinger operators on quantum graphs with identical edges. The spectral problem for the quantum graph is reduced to the discrete magnetic Laplacian on the corresponding combinatorial graph and a certain Hill equation. This may be viewed as a generalization of the classical spectral analysis for the Hill operator to such structures. Using this correspondence we show that ...
متن کاملSpherical and planar folding tessellations by kites and equilateral triangles
We prove that there is a unique folding tessellation of the sphere and an infinite family of folding tessellations of the plane with prototiles a kite and an equilateral triangle. Each tiling of this family is obtained by successive gluing of two patterns composed of triangles and kites, respectively. The combinatorial structure and the symmetry group is achieved.
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ژورنال
عنوان ژورنال: International Journal of Computational Geometry & Applications
سال: 2013
ISSN: 0218-1959,1793-6357
DOI: 10.1142/s0218195913600017