The 105-tooth ring is the odd one out — literally. Its factorization is 105 = 3 × 5 × 7, the only ring in the set with no factor of 2, and that single fact gives it a monopoly: every combination on ring 105 produces an odd petal count. Since petals = 105 ÷ gcd(105, wheel), and 105 is odd, the result is always odd — the full menu is 5, 7, 15, 21, 35, and 105. Five-pointed stars, seven-petal flowers, 35-lobe rosettes: if a pattern looks like something you can't fold in half cleanly, it almost certainly came from this ring.
Ring 105 is also the only ring that reaches its theoretical maximum. Wheels 32, 52, and 64 share no factors with 105 at all (gcd = 1), so each traces all 105 petals before closing — the densest patterns any standard gear pair can draw, needing up to 64 trips around the ring. In the middle of the range, wheel 24 gives an elegant 35-petal star in just 8 rotations, and wheel 30 draws a quick, bold 7-petal flower in 2. The simplest patterns come from wheels 42, 63, and 84 — gcd 21 — each a clean 5-pointed star.
A practical quirk: because so many of its petal counts are prime (5, 7) or products of primes, ring-105 layers rarely align petal-for-petal with layers from other rings — good for organic, woven-looking mandala designs, less good for strict radial symmetry. For evenly nesting layers, use ring 96; for maximum density with odd symmetry, this ring is unmatched. The math behind the odd/even split is worked through on the how it works page.