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On Faces of a Convex Polyhedron in 𝐑3 With a Small Number of Sides

Abstract For any convex polyhedron 𝑃 ⊂ 𝐑3 and for any natural number 𝑘, let 𝐹𝑘(𝑃) denote the number of all faces of 𝑃 with exactly 𝑘 sides. It is well known that 𝐹𝑘(𝑃) ≥ 2 for at least one 𝑘. We consider the question whether 𝐹𝑘(𝑃) ≥ 3, for at least one 𝑘, and present a solution to it. Some related questions are also discussed.