Unfortunately a hexahedron is an ambiguous term. It means a solid object with six plane faces. But that is not enough to uniquely identify shape:
it could be two triangular pyramids with their bases stuck together (a triangular dipyramid), which has 5 vertices (and 9 edges)
or
it could be a pentagonal pyramid, which has 6 vertices (and 10 edges)
or
it could be a parallelepiped (eg cube), which has 8 vertices (and 12 edges).
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It depends on the configuration. Here are some:
A nonagon-based pyramid will have 18 edges and 10 vertices;
An octagon based prism will have 24 edges and 16 vertices;
A pentagon-based dipyramid will have 15 edges and 7 vertices.
There are others.