Collatz and Fibonacci as Dual Operations of Icosahedral Geometry

The Fibonacci recurrence and the Collatz iteration are shown to be dual operations on the same geometric architecture: the icosahedron in D = 3 dimensions with Euler characteristic χ = 2. Fibonacci generates the growth constant φ = (1+√5)/2 from the vertex coordination number √5, with contraction ratio |−1/φ|