# Math Help - convex polyhedron

1. ## convex polyhedron

A convex polyhedron Q has vertices V1, V2, ..., Vn, and 100 edges. The poly-
hedron is cut by planes
P1, P2, ...., Pn in such a way that plane Pk cuts only
those edges that meet at vertex
Vk. 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?

I'm not fully understanding the problem...
I've been working hard on this question so any help would be appreciated.

Thanks.

2. ## Re: convex polyhedron

Let's say $k_i$ edges meet at vertex i. Then cutting the polyhedron at that vertex adds $k_i$ new edges to the new polyhedron, so the total number of new edges is $\sum_{i=1}^n k_i$, for a total of $100 + \sum_{i=1}^n k_i$ vertices in R.

But in the original polyhedron Q, each edge connects two vertices; so $\sum_{i=1}^n k_i = 200$, hence R has 300 edges.

Thanks!!!