• Red gears: 20 teeth, 12 count
• Blue gears: 24 teeth, 20 count
• Yellow gears: 13 teeth, 60 count.
Red gears aligned with icosahedron vertices. Blue gears aligned with dodecahedron vertices. The central rotation axes are aligned with the vertices of a frequency 3v, class-I geodesic tessellation of an icosahedron.
Generalized to higher dimensions: Ball bearings in a hypersphere. That is some mad science.
These guys are selling a 3D-printed version. It's kind of blobby.