Quintic Calabi-Yau manifold 3D mesh
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According to string theory, the universe has ten dimensions: the four of spacetime we experience, plus six more curled up so tightly that we never notice them. In many versions of the theory, those six extra dimensions form a Calabi-Yau manifold, a tiny shape attached to every point of ordinary space, and its geometry determines how strings can vibrate, and so which particles and forces a universe gets. It is still a theoretical proposal awaiting experimental evidence, but a beautiful and mathematically rich one. If you want to admire its geometry (print it out as decoration, drop it into your slides) or play with it in geometry processing, you’re welcome to download the attached .obj file, a 3D mesh of the quintic Calabi-Yau manifold, one of many such shapes string theorists study. Strictly speaking, the mesh is a two-dimensional slice of the full six-dimensional shape, projected into 3D, and squeezing it into our humble three dimensions is what makes it intersect itself, which the real manifold doesn’t. If you use it, please cite “A Construction for Computer Visualization of Certain Complex Curves” by Andrew J. Hanson, which gives the formulas behind the mesh. The file was produced by my friend Thorsten Schimannek, a string theorist who researches and teaches at Utrecht University in the Netherlands, my alma mater. And if you’d like to learn more about Calabi-Yau manifolds, check out Thorsten’s research. And to some experimental quantum physicists out there who take themselves far too seriously: please quit being mean to string theorists, who are doing the most elegant work in physics.