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 intoa closed surface.
The pie-slices have angle and the rectangle haslength 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 thesurface curvature. The total curvature will always be 4.
Sphericon page 6.
Back to Sphericon page 1.