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No because a triangular based pyramid is a tetrahedron that has 4 faces, 6 edges and 4 vertices
A pentagonal based pyramid has 6 faces, ten edges and 6 vertices.
A trangular based pyramid has 4 faces, 6 edges and 4 vertices
A pentagonal based pyramid has 6 faces, ten edges and 6 vertices.
A triangular based pyramid which is a tetrahedron has 4 faces, 6 edges and 4 vertices