SHARYGIN 2009 Problem 23

Is it true that for each $n$ , the regular $2n$ -gon is a projection of some polyhedron having not greater than $n + 2$ faces?

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.