In 2005, Mason Green invented the concept of taking conic sections and attaching them to polyhedra. These were termed "Polycons".
If no constraints are made on how conic sections are attached to polyhedra, there are an infinte number of ways it could be done. I've only included two models but many other interesting ones are possible. This is an area of research for further study.
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| One way to do it is to allow non-convexity. Pictured is a cube with six half Sphericons attached. Adding the half Sphericons gives the model tetrahedral symmetry. One could think of it as a ribbon passing through itself. If one could stand on a cube face, and could pass through the faces, from each cube face there would be a smooth path to four other of the cube's faces. The transparent VRML model is rather interesting as it gives the illusion the internal cube is displayed orthogonally but it is not. |
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| Some of the ones Mason described are convex. This one is called a "Pyricon" for it pyrite symmetry. Place specifically shaped conic sections on twelve faces of an icosahedron and the result is this model. |
Question or comments about the web page should be directed to PolyhedraSmith@gmail.com.
The generation of OFF and VRML files was done with Antiprism. The Hedron application by Jim McNeill was used to generate VRML Switch files.
History:
2024-06-17 Use base.css
2024-06-13 Switch to Multi OFF Viewer
2023-09-01 Switch to Simple OFF Viewer and X_Ite VRML Viewer
2023-03-01 Open Interactive Viewer from model titles
2019-03-12 Changed email address from defunct bigfoot.com
2019-03-07 Switch from Live3D to OFF viewer
2007-09-06 Initial Release
