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In geometry, a developable roller is a convex solid whose surface consists of a single continuous, developable face.[1][2] While rolling on a plane, most developable rollers develop their entire surface so that all the points on the surface touch the rolling plane. All developable rollers have ruled surfaces. Four families of developable rollers have been described to date: the prime polysphericons,[3] the convex hulls of the two disc rollers (TDR convex hulls),[4] the polycons [5][1] and the Platonicons.[2][6]
- ^ a b Hirsch, David (2020). "The Polycons: The Sphericon (or Tetracon) has Found its Family". Journal of Mathematics and the Arts. 14 (4): 345–359. arXiv:1901.10677. doi:10.1080/17513472.2020.1711651. S2CID 119152692.
- ^ a b Seaton, K. A. "Platonicons: The Platonic Solids Start Rolling". Tessellations Publishing.
- ^ "Polysphericons". h-its.org. Heidelberg Institute for Theoretical Studies.
- ^ Ucke, Christian. "The two-disc-roller — a combination of physics, art and mathematics" (PDF). Ucke.de.
- ^ "Polycons". h-it.de. Heidelberg Institute for Theoretical Studies.
- ^ "Platonicons". 2020.bridgesmathart.org. The Bridges Organization.