Drag to rotate. Explore torus, Klein bottle, Boy surface, Roman surface and more. These are surfaces that cannot be embedded in 3D without self-intersection — windows into higher dimensions.
Torus: x=(R+r·cos v)cos u, y=(R+r·cos v)sin u, z=r·sin v. Genus 1 surface. Euler characteristic χ=0. Flat torus (square with opposite sides identified) is the 2D analog of a donut.