Centroids and vertices live in Q(√5)². Rotations by 72° are exact via cos(72°) =
(√5−1)/4, sin(72°) = √(10+2√5)/4 (the radical is stored symbolically as
S72 with S72² = (10+2√5)/16).
For general n-gons, floating-point arithmetic is used with double precision. The
Sierpiński triangle uses an IFS (iterated function system) with contraction ratio ½.