The Euler characteristic requires that
Vertices + Faces = Edges + 2
Here that would require 6 + 7 = 15 + 2 or 13 = 17 which is clearly not true. So there cannot be a polyhedron with the stated configuration.
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No. The numbers are not consistent with the requirements of the Euler characteristic.
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7 faces. 10 vertices. 15 edges.
It has 7 faces, 10 vertices, and 15 edges
It has 7 faces, 15 edges and 10 vertices