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Developable Rolling Solids

The main mathematical news

1929: The Oloid was discovered by Paul Schatz.
1980: David Hirsch patented a form that is now known as The Sphericon
2006: Tony Phillips and David Springett introduced a generalization of the sphericon – The Poly-Sphericon family.
2019: David Hirsch published The Polycon family, another generalization of the sphericon
2020: David Hirsch came out with another discovery of a new family of developable rollers, called the Platonicon Family.

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Additional Theorems / conjectures / Open questions

* A cube has 11 different planar nets
* The sphericon is a single-faced developable roller that can be created without relying on the convex-hull. While rolling Its center point maintains a constant height.
* Shephard’s Conjecture: All convex polyhedrons can be developed in
at least one way, by cutting across their edges.

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The main mathematical concepts / Principles

52B99; 97G30, 97G40
3-D Geometrical solids
Developable solids
Developable rollers
Platonic solids
Rolling solids
Single faced solids
Convex hull

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