A convex polyhedron Q has vertices V_{1}, V_{2}, \ldots, V_{n}, and 100 edges. The polyhedron is cut by planes P_{1}, P_{2}, \ldots, P_{n} in such a way that plane P_{k} cuts only those edges that meet at vertex V_{k}. In addition, no two planes intersect inside or on Q. The cuts produce n pyramids and a new polyhedron R. How many edges does R have?
Answer Choices
A. 200
B. 2 n
C. 300
D. 400
E. 4 n