The Differential Geometry of the Sphericon


7. Further projects

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.

cutout of hexasphericon

The pie-slices have angle pi x sqrt(3)/2 and the rectangle has length equal to the round side of a pie-slice.

Two views of the Hexasphericon

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 4pi.

Back to Sphericon page 6.

Back to Sphericon page 1.

© copyright 1999, American Mathematical Society.