SHARYGIN 2006 Problem 10

At what $n$ can a regular $n$ -gon be cut by disjoint diagonals into $n- 2$ isosceles (including equilateral) triangles?

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.