The classic Geomag bars are approximately 27mm long and the new ones are 58mm,
the balls remain 12.7mm diameter.
Rounding slightly: that's 1" for old bars, 2-1/4" for new bars, and 1/2" balls.
For polyhedron building, what matters is the "distance between centers" which is,
therefore, 1-1/2" for classic and 2-3/4" for kids.
The ratio between these two is 11:6 (1.83) which isn't close to any
useful ratio I can think of.
Two ratios that would have obvious uses are: the cube diagonal (1.73) and the
golden ratio (1.61).
I happen to have a few 3/4" balls and see that for this size of ball the ratio is 1.71.
Here's a pentagram with 3/4" balls:
See that the edges aren't quite straight. Also, at the sharp points the balls don't quite seat correctly because the rods interfere with each other.