cairo torus

thingiverse

This mesmerizing creation is a stunning Cairo pentagonal tiling of intricately designed pentagons projected onto the surface of a majestic torus. Find the ingenious OpenSCAD code at http://www.whitehydra.com/cairo_torus.html Post-Printing It was expertly printed on a state-of-the-art MakerBot Replicator at school, with no supports whatsoever. How I Designed This Masterpiece First, I skillfully coordinated the vertices of a single hexagon, plus the five lines inside it. The coordinatization was beautifully done in R2 in the x-y plane. I defined elegant lines connecting each vertex with a loop that translated multiple spheres along those lines. I utilized the vector equation of a line: V = v0 + t(v1 - v0), where v0 and v1 are the two vertices on either end of the line. I re-parameterized each line into toroidal coordinates in order to project each line out onto the surface of a magnificent torus. After I had the first pattern on the torus, I was able to rotate and copy the pattern all the way around the majestic torus.