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- W2953175094 abstract "The uniqueness of the orthogonal Z^gamma-circle patterns as studied by Bobenko and Agafonov is shown, given the combinatorics and some boundary conditions. Furthermore we study (infinite) rhombic embeddings in the plane which are quasicrystallic, that is they have only finitely many different edge directions. Bicoloring the vertices of the rhombi and adding circles with centers at vertices of one of the colors and radius equal to the edge length leads to isoradial quasicrystallic circle patterns. We prove for a large class of such circle patterns which cover the whole plane that they are uniquely determined up to affine transformations by the combinatorics and the intersection angles. Combining these two results, we obtain the rigidity of large classes of quasicrystallic Z^gamma-circle patterns." @default.
- W2953175094 created "2019-06-27" @default.
- W2953175094 creator A5000134213 @default.
- W2953175094 date "2010-01-20" @default.
- W2953175094 modified "2023-09-27" @default.
- W2953175094 title "Rigidity of quasicrystallic and Z^gamma-circle patterns" @default.
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