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Build a Sphericon. Build two and roll them together (see Ian Stewart's column for more ideas.)
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.
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