Gallery of flat tori realized as Hopf surfaces in the 3-sphere, one for each lattice type
A gallery of flat tori realized as Hopf tori in S3 and stereographically projected into R3, rendered with pathtracing. Each torus corresponds to a different lattice Λ=Z⊕Zτ in the upper half-plane, including τ=i (square), τ=i2 (rectangular), τ=2−1+i3 (hexagonal), τ=2−1+i7, and τ=2−1+i11.
For each lattice, the program displays the fundamental parallelogram, a gridline pattern, and the Hopf preimage of a curve on S2. The pathtracer provides realistic global illumination, revealing the smooth geometry of these surfaces in R3.
Controls: Click and drag to orbit, scroll to zoom.
