A pyramid with an n-sided base will have n + 1 vertices, n + 1 faces, and 2n edges.
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The given description fits that of a triangular based pyramid which has 4 faces, 6 edges and 4 vertices
Triangles.
A square pyramid has 5 faces , 5 verticies and 8 edges
8 lateral faces and a base
A square pyramid, or square-based pyramid, has 5 faces and 8 edges. One face forms the square base, and there are four triangular faces.