Clifford Torus

clifford cyclides morph 019
The Clifford Torus is the torus S^1/sqrt(2) x S^1/sqrt(2) in R^2 x R^2 = R^4. It actually lies in the unit sphere S^3 from where it can stereographically be projected into R^3. The animation shows how projections from different points of R^3 look. When the projection center is on the Clifford Torus then the image looks like a plane with a handle.
clifford torus st
clifford torus st
clifford torus sw
clifford torus sw

Clifford_Tori.pdf