Hyperbolic Planar Tesselations Here are pictures of some regular tesselations of the hyperbolic plane. Each tesselation is represented by a Schlafli symbol of the form {p,q}, which means that q regular p-gons surround each vertex. There exists a hyperbolic tesselation {p,q} for every p,q such that (p-2)*(q-2) > 4. Each tesselation is shown in various stages of truncation. The dual of each tesselation or truncated tesselation is shown in blue. You may want to make your browser window wide so you can see them all at once. Here are some more semiregular hyperbolic tesselations, based on regular hyperbolic tesselations. Note that the ones based on a regular {p,q} are the same as the ones based on a regular {q,p}, but shown in a different orientation. A tesselation (a.k.a. tiling) is uniform if its faces are regular and its symmetry group (including reflections) is transitive on the vertices. Fundamental Tilings (p0|p1|... Start with any cyclic ordered list of integers p0,p1,...,pn-1 (n>=3, pi>=2). Snub Tilings, (p0||p1||...
Trenelle: territoire bricolé Adrienne Froemelt - Scripting Fibonacci Recent explorations of the Fibonacci sequence and logarithmic spirals have led to this design scripting generation. Using Rhinoscript, I wrote of a function that uses Binet's Formula to find the nth Fibonacci number. The function takes in a user input for the number of integers of the Fibonacci sequence. From there, the Fibonacci spiral is drawn, and the spiral is manipulated through projections and rotations that eventually form the wireframe of a sphere. A piping function is applied to the wireframe to give three-dimensionality. The Fibonacci Weaving Façade is a system of interpolated curves that network to form a structural mesh.
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