No. The given numbers do not satisfy the Euler characteristic for a simply connected polyhedron.
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A pentagonal pyramid.
There can be no such polyhedron since the given numbers are not consistent with the Euler characteristic.
Not any normal polyhedron since the numbers are contary to the Euler characteristic.
A pentagonal pyramid has 6 faces, 6 vertices and 10 edges.
A pentagonal prism has 7 faces, 10 vertices and 15 edges.