# The polycons: the sphericon (or tetracon) has found its family

@article{Hirsch2019ThePT, title={The polycons: the sphericon (or tetracon) has found its family}, author={David Hirsch and Katherine A. Seaton}, journal={Journal of Mathematics and the Arts}, year={2019}, volume={14}, pages={345 - 359} }

This paper introduces a new family of solids, which we call polycons, which generalize the sphericon in a natural way. The static properties of the polycons are derived, and their rolling behaviour is described and compared to that of other developable rollers such as the oloid and particular polysphericons. The paper concludes with a discussion of the polycons as stationary and kinetic works of art. GRAPHICAL ABSTRACT

#### 2 Citations

Compact Shape Morphing Tensegrity Robots Capable of Locomotion

- Medicine, Computer Science
- Front. Robot. AI
- 2019

A design methodology for fabricating tensegrity robots of varying morphologies with modular components is introduced and two resulting robots—the Icosahedron and the Sphericon Tensegrity Robots—display shape morphing (packing-unpacking) capabilities and achieve locomotion through internal mass-shifting. Expand

Platonicons: the Platonic solids start rolling

- Mathematics, Physics
- 2020

We describe the construction of a new family of developable rollers based on the Platonic solids. In this way kinetic sculptures may be realised, with the Platonic solids quite literally in their… Expand

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