Sphericon

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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. It was first introduced by the Israeli game and toy inventor David Haran Hirsch who patented it in Israel in 1980.[1] It was given its name by Colin Roberts, of Hertfordshire, England, who also explored it.

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 sectors (with central angles π/√2) joined edge-to-edge [1].

Like the Oloid and other developable rollers, 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.

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