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There is no such polyhedron. The numbers given in the question do not satisfy the Euler characteristic for simply connected polyhedra.

Alternatively, the fact that it has eight faces means that is should be an octahedron. However, among the 257 topologically distinct convex octahedra, the maximum number of vertices is 12 and the maximum number of edges is 18. Both these numbers are well below what you require!

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9y ago

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