A triangular pyramid has four vertices. Picture a "regular" triangle. There are three sides, and three vertices. Now pick a point "behind" the triangle, and connect that point to each of the three vertices of the triangle. That fourth point is the fourth vertex of the triangular pyramid you have just constructed.
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It has 8 vertices.
If it is a 2-dimensional figure then it is a quadrilateral. If it is a 3-dimensional figure then it is a tetrahedron.
vertices
A sphere.
A square based pyramid