A vertice is a point where two or more lines connect. If an object is a closed object, meaning that all the line's endpoints are connected to another line's endpoint without any openings, then the object has as many vertices as it does lines. A square has four lines so it has four places where lines meet, called vertices. So a square has four vertices.
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A square prism has 8 vertices.
A square pyramid has 5 vertices.
A cuboid has 8 vertices - whether it is square-based or not.
A square based pyramid has 5 vertices.
a pyramid will have the same number of vertices as corners of the base + 1 so a square pyramid is (4 corners on a square) + 1 = 5 vertices