# Farey sunburst

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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 entries where 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 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).