No. A cone could be considered the limiting case of a pyramid, but a hemisphere is not, because the lines joining the base to the apex are not straight.
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In geometry, pyramid has many forms such as rectangular pyramid, trapezoidal pyramid, quadrilateral pyramid and even triangular pyramid. Triangular pyramid is a pyramid with triangular base and can be called as a tetrahedron if each of its faces has congruent equilateral triangles.
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A square pyramid is a pyramid whose base is in the shape of a square.
Square Pyramid
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