I believe that such an object cannot exist in normal 3-d space. If there are 6 vertices, the maximum number of edges is 12.
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6 faces 10 vertices 15 edges
A pentagonal based pyramid has 6 faces, ten edges and 6 vertices.
A pentagonal pyramid has 6 faces, 6 vertices and 10 edges.
Faces: 6Vertices [or corners]: 8Edges: 12eight.
9 edges, 6 vertices