The sphericon is a solid that has a continuous developable surface with two congruent semi circular edges, and four vertices that define a square. It is a member of a special family of rollers that, while being rolled on a flat surface, bring all the points of their surface to contact with the surface they are rolling on. It was first introduced by the Israeli game and toy inventor David Haran Hirsch who patented it in Israel in 1980. It was given its name by Colin Roberts, who also explored it.
It may be constructed from a bicone (a double cone) with an apex angel 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.
The surface area of a sphericon with radius r is given by:
The volume is given by:
exactly half the volume of a sphere with the same radius.
- "Mathematical Recreations: Cone with a Twist", Scientific American, October 1999
- David Haran Hirsch (1980): "Patent no. 59720: A device for generating a meander motion; Patent drawings; Patent application form; Patent claims
- Paul J. Roberts (2010). "The Sphericon". Archived from the original on 2012-07-23.
- A mesh at www.pjroberts.com/sphericon, archived by web.archive.org
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- Sphericon construction animation at the National Curve Bank website.
- 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