Sphericon Balance Ball

The Sphericon is a geometric solid with a bicone-like shape, but with a twist that allows it to roll in a serpentine line instead of a circle. (See link for a picture of a sphericon.)

When a sphericon rolls, it has periodic points in the path where the curve is very sharp. At these points, the rolling sphericon tends to slow down, but it will keep rolling. (see link for picture of sphericon path)

If you had a sphericon big enough to stand on (say 18 inches in diameter) then you could hop on top and, with little kicks, get the sphericon rolling and keep it rolling in its peculiar meandering way. This would be fun in the same way learning the hoola hoop or yo-yo is fun. It would be a good form of aerobic exercise, because it is low-impact (unlike running and jumping-rope.)

Balance-walking on the sphericon looks like balance-walking on a ball, but it's easier. A ball is tangent with the ground at a single point, but the sphericon is always tangent with the ground along a line. This makes it more stable than a rolling ball. Deep ridges along the curves give you a good toehold.

The sphericon's tendency to hesitate will help beginners feel safe. The sphericon won't run away with them on flat ground. If the beginner has trouble getting the sphericon moving, he can try gradually sloped ground.

Once the sphericonner has confidence, he should be able to roll a complete revolution of the sphericon in four precisely placed steps. He can participate in sphericon races, or just roll around the neighborhood amazing his friends. With practice, she can go on to freestyle and extreme sphericonning - challenges like steeper slopes, rough terrain, and skate parks.

Sphericon roller toys will be weighted to maximize fun and safety, and covered with soft rubber tread that follows the direction of the rolling surface. Beginners should wear protective gear (as rollerskaters do).