Problem

Source: 7th Iranian Geometry Olympiad (Intermediate) P5

Tags: 3D geometry, geometry, IGO



Find all numbers $n \geq 4$ such that there exists a convex polyhedron with exactly $n$ faces, whose all faces are right-angled triangles. (Note that the angle between any pair of adjacent faces in a convex polyhedron is less than $180^\circ$.) Proposed by Hesam Rajabzadeh