Sphericon

A sphericon, with each identical half shown in a different color. Paper Sphericon

The sphericon is a three-dimensional solid with one side and two edges, discovered by Colin Roberts, of Hertfordshire, England.

It may be constructed from a bicone (a double cone) with an apex of 90 degrees, by splitting the bicone along a plane through both apexes, rotating one of the two halves by 90 degrees, and reattaching the two halves.

Alternatively, the surface of a sphericon can be formed by cutting and gluing a paper template in the form of four circular wedges (with angles of $180 / \sqrt{2}$ degrees) joined edge-to-edge [1].

When rolled on a flat surface, every point on the surface of a sphericon comes in contact with the surface it is rolling on.

Ian Stewart of the University of Warwick and Tony Phillips of Stony Brook University have also investigated the sphericon, and it has helped the latter develop theories about mazes.

References

• Mathematical Recreations - Cone with a Twist, Scientific American, October 1999

External links

• Sphericon Homepage. It contains images, text and animation that give a fuller view of the sphericon family.
• Paper model of a sphericon Make a sphericon
• Sphericon variations using regular polygons with different numbers of sides
• A Sphericon in Motion showing the characteristic wobbly motion as it rolls across a flat surface