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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A polyhedron has 30 edges and 12 vertices. How many faces does it have
A sphere is not a polyhedron because it has no edges, no vertices and no flat faces The word 'polyhedron' means many faces.
eight
In geometry, a pentahedron is a polyhedron with five faces. That can either be a square pyramid with 5 vertices, 8 edges and 5 faces or a triangular prism with 6 vertices, 9 edges and 5 faces.
A sphere has no faces, no edges, and no vertices.