Farey sunburst

The Farey sunburst of order 6

The order-n Farey sunburst is a certain non-convex simple polygon with vertices located at integer coordinates. It is constructed as follows:

• Create the order-n Farey sequence by listing all distinct fractions a/b where 0 ≤ a ≤ b ≤ n and b ≠ 0, selecting only fractions in lowest terms and sorting them in increasing order. There will be $1+\Phi (n)$ entries where $\Phi$ denotes the totient summatory function.
• Interpret each fraction a/b as a point with Cartesian coordinate (a,b), and connect consecutive points with line segments. The result is a path starting at (0,1) and ending at (1,1).
• Reflect this path along the x-axis, y-axis, and the two diagonals x = ±y to form a closed polygon with square symmetry.

It has $8\Phi (n)$ vertices. All Farey sunbursts are non-self-intersecting. The interior of a Farey sunburst contains only a single point with integer coordinates, which is (0,0).