The Sphericon
In the 1960's C.J. Roberts invented the "Sphericon". The first Sphericon model he made was of Mahogany which was given to his sister and the topic was forgotten. In May of 1999, Roberts wrote to Ian Stewart, a writer for Scientific American and in October 1999, Stewart published an article titled "Cone with a Twist". This was the first time most people learned of the Sphericon's existance.
Links to other pages for further reading:
A smooth Sphericon is made from a bicone. As such, the base model being two cones joined at the base, it is not a polyhedron.
A type of Sphericon can be made from a dipyramid. In the N-icon Study, higher order N-icons are built programmatically from polygons and are thus, all faceted. If the faceting is ignored they are still valid models for the study of their conic counterparts.
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| A Sphericon can be made of a bicone or any dipyramid with a 90° apex has been divided in two such that its cross section is a square. Here is a split dipyramid displayed in LiveGraphics3D. (see this page for how to control a Live3D graphic with your mouse). |
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| One of the two parts is rotated 90° then the two parts are reassembled. In this LiveGraphics3D image, the half on the right side has been rotated. |
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The assembled Sphericon. In this form the Sphericon would be what Roberts calls a "Faceted Sphericon". The Faceted Sphericon lends itself to be easily modeled since most computer modeling is done with polygons. A dipyramid will be made of isosceles triangles and the more facets the dipyramid has, the smoother the Faceted Sphericon model will be visually.
The Sphericon has one continuous surface and two discontinuous edges. |
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| A nearly Smooth Sphericon can be modeled by increasing the number of facets to a very high number. This "Smooth" Sphericon is made of a total of 576 isosceles triangles. |
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The dual of a bicone is a cylinder. The dual of the Sphericon can be constructed from a cylinder such that its width and length are equal. Then one half is turned 90° and the halves are rejoined just as they were in building the Sphericon.
The dual of the Sphericon has two discontinous surfaces and one continuous edge. |
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Question or comments about the web page should be directed to polyhedra@bigfoot.com.
The generation of OFF, VRML, and Live3D files was done with
antiprism. The
Hedron application by
Jim McNeill was used to generate VRML Switch files.
History:
2007-09-06 Initial Release
