Hyperspace Flows · 4D
Clifford Torus
A flat torus inside the 3-sphere
In four dimensions a torus can be perfectly flat, with no stretching at all. Rotate it through W and it turns itself inside out.
- Curvature
- 0
- Lives on
- S³
Watch it turn through the fourth dimension, hear the chord of its edges, and slice it with our space to see it pass through.
Facts
- Every point is (cos a, sin a, cos b, sin b) ÷ √2: two circles multiplied.
- It splits the 3-sphere into two identical solid tori.
- Projected into 3D it becomes an ordinary ring torus.
Across the dimensions
- Grows from TorusIn four dimensions a torus can be perfectly flat: the Clifford torus.
- Grows from Horn TorusIn four dimensions a torus can be perfectly flat: the Clifford torus.
