The 96-tooth ring is the workhorse of every Spirograph set — the ring most instruction books start with, and the one this site uses for its default 96/45 pattern. Its personality comes from its factorization: 96 = 2⁵ × 3. That heavy load of 2s means 96 shares a factor with every single wheel in the set, so no combination ever reaches the theoretical 96-petal maximum. What you get instead is a tidy ladder of petal counts — 2, 3, 4, 6, 8, 12, 16, 24, 32, and 48 — almost all of them even, which is why ring-96 patterns tend to look balanced and symmetric rather than star-like.
The petal count follows one rule: petals = 96 ÷ gcd(96, wheel). The densest pattern comes from wheel 50, whose only shared factor with 96 is 2, giving 48 petals over 25 rotations — the closest thing to lace this ring produces. Wheels 45, 63, and 75 all share exactly a factor of 3, so each gives a classic 32-petal rosette with a different petal shape (the smaller the wheel, the pointier the petal). At the other extreme, wheel 48 divides 96 perfectly — gcd 48 — and closes after a single lap with just 2 petals, and the powers of two (wheels 32 and 64) produce the ring's only odd counts: soft 3-petal triangles.
Because its petal ladder is so evenly spaced, ring 96 is the best ring for layered designs: 8-, 16-, and 32-petal patterns nest inside each other with aligned symmetry, which is why most of the printable mandala coloring pages on this site are built on it. If you want odd, prime-flavored star counts instead, that's ring 105's specialty.