Since each triangular face will have a base at an edge of the hexagon base, there will be 6 triangular faces and 1 hexagon at the base. Each triangle will have an edge at the base that it shares with the hexagon. Each triangle will have two other edges that it shares with the two adjacent triangles. We can thus get the number of edges by counting the number of triangles and then add the number of base edges - 6 + 6 = 12.
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A hexagon based pyramid has 7 corners.
A square based pyramid has 8 edges and 5 faces.
There are many possibilities. Some of them are: A nonagon-based pyramid. A hexagonal prism. A hexagonal dipyramid (two hexagon-based pyramids stuck together on their bases).
Six edges.