An ordinary cone placed on a flat surface rolls around in circles. A double-cone can roll in a clockwise circle or a counterclockwise one. A sphericon, in contrast, performs a controlled wiggle, with first one conical sector in contact with the flat surface, then the other. Two sphericons placed next to each other can roll on each other's surfaces. Four sphericons arranged in a square block can all roll around one another simultaneously. And eight sphericons can fit on the surface of one sphericon so that any one of the outer solids can roll on the surface of the central one.
The sphericon was first found by the Englishman Colin Roberts in 1969, while he was still in school. In 1999 he brought his discovery to the attention of Ian Stewart who subsequently wrote about the new object in his "Mathematical Recreations" column in Scientific American.1
Related category SOLIDS AND SURFACES
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