A pyramid with an n-sided base will have n + 1 vertices, n + 1 faces, and 2n edges.
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An octagonal pyramid has 9 faces, 9 vertices, 16 edges.
You cannot. For example: 6 faces can be a cuboid (8 vertices and 12 edges) or it can by a triangular di-pyramid (5 vertices, 9 edges). Incidentally, a triangular di-pyramid is just two triangular pyramids stuck together at one face.
no numbers have the same number of edges and vertices
A triangular dipyramid (two tetrahedrons or triangular pyramids stuck together) has 9 edges and 5 vertices. A parallelepiped (including cuboid) has 12 edges and 8 vertices
for any prism , number of ___ + number of vertices = number of edges + ___