Creating a Polyhedron

Polyhedra are solids formed by polygons that share a common side. Consider various polyhedra (e.g., tetrahedron (4 faces), hexahedron (6 faces), octahedron (8 faces)).

What is the least number of polygons that can share a common vertex and still form a polyhedron? What restriction must be met regarding the sum of the angles at this vertex in order for a polyhedron to be formed?