Constructing a Hyperbolic Lattice | hypertiling скачать в хорошем качестве

Constructing a Hyperbolic Lattice | hypertiling

Let us construct a hyperbolic tiling in the Poincare disk representation! We start by choosing the number of edges per cell to be p = 7 and the number of cells that meet in each vertex to be q = 3. The first layer consists of only one polygon, the center polygon. Our algorithm exploits the p-fold rotational symmetry of the lattice by tesselating only 1/p-th of the disk (a "sector") and then replicating this sector around the disk using discrete rotational transformations. Since only one polygon of layer two lies in our sector, we readily continue with the next layer. New cells are constructed by rotating all cells of the previous layer around each of their vertices. For more information visit our website: http://www.hypertiling.de #hyperbolicspace #poincaredisk #hyperbolictiling