The Sphericon has four cone-points and two arcs of zip-loci. Otherwise it has no curvature, since it can be assembled from flat pieces without stretching.

- At each cone-point there is a concentration of curvature
equal to -. Total contribution from cone-points:
4 - 4.
- If the common radius of the cones is R, then each component
of the zip-locus has length R. Since a length L of zip-locus
carries a concentration 2L/R of curvature, each component of the
zip-locus contributes 2L/R x R = 2 of curvature. Total
curvature carried by the zip-locus: 4.
- Total curvature of the Sphericon: 4.

On to Sphericon page 7.

Back to Sphericon page 5.

© copyright 1999, American Mathematical Society.