cut-and-project

A free browser geometry builder from 1D to 6D: 1D+ (a Morse line, and Construct: square to tesseract, Kagome to hyper-pyrochlore, rhombus to RD), tilings, a kaleidoscope, nets that fold into solids, RD lattices, the Euclid–Kepler–Pacioli cell, 4D polytopes, Penrose/icosahedral quasicrystals, Shells. Twin of Polyhedraverse.

The official computational simulation lab for the Helix-Light-Vortex (HLV) framework. We translate 6D cut-and-project geometries into reproducible 3D quasicrystalline G-lattices to rigorously stress-test effective field models, weighted graph Laplacians, and topological vortex stability.

Period formulas for one-dimensional cut-and-project gap sequences, with explicit rational-slope formulas and the complementary irrational aperiodicity statement formalized in Lean 4.