These three gears hold themselves together without an axle or a frame, like our "Gripping gears" (https://www.youtube.com/watch?v=RBZG8M8_a8Y). But these can change how they are connected together - in fact they can "braid" around each other however you like. Shapeways 3D printed version: http://shpws.me/SXbE This video was filmed during ICERM's Fall 2019 "Illustrating Mathematics" program, which was made possible through the support of - The National Science Foundation (Grant Number DMS-1439786) - The Alfred P. Sloan Foundation (Grant Number G-2019-11406) - A Simons Foundation Targeted Grant to Institutes (Award ID 546235)