A sphericon is a really cool shape, fun to hold, roll, or just look at.
You can find find more information on the sphericon shape from Paul J. Roberts http://www.pjroberts.com/sphericon/
This instructable is designed for folks with some handbuilding experience in ceramics. If you have some pottery skills but are new to handbuilding, try to practice some of the basic skills of slab work before attempting to build your own sphericon. There is a listmania of recommended books for handbuilders on Amazon.com here
Some new photos added, including a view of the bisqued piece made in the course of this instructable. Hey, and now we have a picture of the final item after firing to cone 10 in gas reduction! I wiped most of the glaze off before it went in the kiln.