A square based pyramid has 5 vertices.
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A triangular based pyramid has 4 vertices.
A square pyramid has a square base and four triangular sides. This gives it five faces, eight edges and five vertices.
A triangular based pyramid has 4 facxes, 4 vertices and 6 edges
4
It depends on the shape of the base. A pyramid that has a base with n vertices (an n-gon) will have n+1 vertices in all.