Build a Hexasphericon: assemble two copies of this shape into a closed surface.
The pie-slices have angle and the rectangle has length equal to the round side of a pie-slice.
Notice that this solid has a left-hand and a right-hand form, whereas the Sphericon does not.
Generalize this construction to make more complicated solids. Gauss' Theorem can always be used to locate and calculate the surface curvature. The total curvature will always be 4.
Back to Sphericon page 1.