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The number of vertices on a solid pyramid will depend on its base as for example if it is a triangular based pyramid (tetrahedron) then it will have 4 vertices, 6 edges and 4 faces.
A tetrahedron or triangular pyramid.
A triangular pyramid.
A tetrahedron or triangular-based pyramid has four faces, six edges, and four vertices.
Assuming that each vertex is used to connect exactly two sides, all two-dimensional shapes will have the same number of sides as vertices. So a shape with 4 sides will have 4 vertices and a shape with 3 sides will have 3 vertices. Think of a square (4 sides, 4 vertices) and a triangle (3 sides, 3 vertices).