Mobile Icosapods
Matteo Gallet, Georg Nawratil, Josef Schicho, J.M. Selig

TL;DR
This paper characterizes the complete set of mobile 20-pods, a class of mechanical devices with a maximum of 20 legs, and demonstrates the possibility of constructing such pods with all real coordinates.
Contribution
It proves that Borel's 1904 construction encompasses all mobile 20-pods and shows they can be realized with real coordinates.
Findings
Borel's construction characterizes all mobile 20-pods.
All mobile 20-pods can be realized with real coordinates.
The maximum number of legs for a mobile pod is 20.
Abstract
Pods are mechanical devices constituted of two rigid bodies, the base and the platform, connected by a number of other rigid bodies, called legs, that are anchored via spherical joints. It is possible to prove that the maximal number of legs of a mobile pod, when finite, is 20. In 1904, Borel designed a technique to construct examples of such 20-pods, but could not constrain the legs to have base and platform points with real coordinates. We show that Borel's construction yields all mobile 20-pods, and that it is possible to construct examples with all real coordinates.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
