Steve Trettel

MediumComputer generated using a custom-built shader material and THREEjs.
The ArtThe flat torus which comes from identifying opposing sides of a hexagon, isometrically embedded in 4-space and viewed under stereographic projection. The torus is parameterized by drawing a closed curve on the 2-sphere, and then taking the preimage under the Hopf map.
The MathThe torus admits many inequivalent flat metrics (choose a parallelogram, and abstractly identify pairs of opposing sides). Most of these tori do not have any special symmetries, but two of them, called the square and the hex torus (because they can also be constructed by folding up a square or hexagon, respectively) are especially symmetric.
CategoriesDifferential Geometry, Computer Graphics, Math Illustration, Stereographic Projection