Discussion

The number of edges of a polyhedron, which has 7 faces and 10 vertices, is

Answer: C

The polyhedron has 15 edges.

Euler's formula connects the faces F, vertices V and edges E of any convex polyhedron.

\[ \begin{aligned} F + V - E &= 2 \\ 7 + 10 - E &= 2 \\ E &= 15 \end{aligned} \]

A pentagonal prism is an example: 7 faces (two pentagons and five rectangles), 10 vertices and 15 edges.

17 is \(F + V\) without subtracting 2. With 13 or 14 edges, \(F + V - E\) would be 4 or 3, not 2, so no polyhedron has those counts.

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