pentadecahedron
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No. Even though I do not know the correct answer, I do know that that is not the correct answer.
A pentadecahedron has 15 faces - NOT 15 edges. Polyhedra often have names with Greek prefices which refer to the number of faces.
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Octagonal prism
A 3D shape that has 6 edges is called a hexagonal prism.
retangle
A pentagonal prism will have 15 edges.
There is no limit to the number of vertices nor edges.