Flipping Polygons

The Fibonacci numbers is the series of numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, ... The next number is found by adding up the two numbers before it. A Fibonacci polygon is a polygon whose number of vertices is a Fibonacci number. You are given an array of $N$ regular Fibonacci polygons, where each polygon is a regular $A_i$-gon. The vertices of this $A_i$-gon are numbered from $1$ to $A_i$ in clock