Z/12Z ≅ Z/4Z × Z/3Z

A 12-hour clock and its image under the isomorphism from Sunzi's Theorem, embedded on a torus.

Z/12Z
0
n mod 12
Z/4Z × Z/3Z
(0, 0)
(n mod 4, n mod 3)
Drag the torus to rotate
30%

The dashed curve is the lift of the diagonal s ↦ (s·2π/4, s·2π/3) for s ∈ [0,12] — a (4,3)-torus knot. Its 12 evenly-spaced sample points are exactly the lattice points (n mod 4, n mod 3). Since gcd(4,3) = 1, the curve is a single closed loop visiting all twelve points. Each hour n on the clock shares its color with the corresponding point on the torus.