An equilateral triangle-shaped board is covered with $3n$ triangular tiles on the edges and $\frac{n(n-1)}{2}$ hexagonal tiles inside, as in the visualization. Find all n for which a closed polyline can be created from red edges by rotating the hexagons.

• to rotate the hexagon, click on it
• n can be changed in the top bar
• the top bar contains information whether a closed polyline is created