The Differential Geometry of the Sphericon
6. The total curvature of the Sphericon
According to the Gauss-Bonnet Theorem, the total curvature of a smooth convex surface is 4. We can check that this statement holds for the more exotic curvature of the Sphericon.
The Sphericon has four cone-points and two arcs of zip-loci.Otherwise it has no curvature, since it can be assembled fromflat pieces without stretching.
Sphericon page 7.
Back to Sphericon page 5.