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By the requirements of the Euler characteristic,

E + 2 = V + F

That is, 24 + 2 = V + 16

So that V = 10.

The shape is a dipyramid with a octagonal base. That is, two octagonal-based pyramids stuck together at their bases.

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Q: How many vertices does a polyhedron with 16 faces and 24 edges have?
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