All the Daisy Wheels intersect at the center point in the Dandelion Sphere.
Each point on the outside of the Sphere is the intersect of 3 "wheels". 12 cubed.
3 is the magic number because we're dealing with equilateral triangles that make up a regular tetrahedron. Three lines meeting at 60 deg. just like the Daisy Wheel.

If you take 3 equilateral triangles or half a Daisy Wheel and cut them out and fold them to make a 3D object (a regular tetrahedron), You magically get a fourth equilateral triangle. 3 x 4 = 12

3 x 3 x 3 = 27. or 3 cubed ( there's the 27 ) and 3 cubed x 64 = 12 cubed

Remember thats One, Two, Three. Three licks to the center of a Tootsiepop. very important.

Lest we not forget, Daisy Wheels have 6 points and everything is 60 deg., and then they have a dark side or Yin to their Yang, 6 points half way in between, That makes 12 and also gives us 30 & 90 deg. If you divide the wheel again you get 24 points and 15 & 45 deg. If you divide the Daisy Wheel any further you get nothing but nasty fractions, 22 1/2, 11 1/4, 5 5/8, ...... Not much use to a carpenter, unless you are doing mitre cuts, then it's exactly what you need. I'd be hard pressed to set my Starrett protractor to 5/8 of a deg.

The axle width combined with wheel offset determines the space between your wheels. If the wheels have to much back spacing they may not clear your brake calipers.

Happy Wheelin'