A polyhedron has the property that three edges intersect in six of its nodes, while four edges intersect in the remaining node, what are the number of edges and faces in the polyhedron?
I've gone this far
$$2E = 3\cdot 6 + 4\cdot 1 = 22 \Rightarrow E = 11$$
Then Euler's formula gives $$V-E+F = 7 - 11 + F = 2 \Rightarrow F =6. $$
So we have $11$ edges and $6$ faces.
Is this correct ?