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MathNet 2011 Question 17

Math Olympiad Vault · MathNet 2011

Question 17

A convex polyhedron has $100$ edges. All its vertices are cut off close to the vertices with a sharp flat knife, so that the cutting planes do not intersect inside or on the boundary of the polyhedron. For the resulting polyhedron, calculate:
(a) the number of vertices;
(b) the number of edges.

How many faces does this new polyhedron have?