Yes because it has many faces which is the meaning of a polyhedron
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It can be any type of pyramid.
Yes when in the form of a tetrahedron which is a triangular based pyramid
A square based pyramid.
A regular polyhedron has equal size faces as in the case of a tetrahedron which is a triangular base pyramid that has 4 equilateral triangle faces.
Any. You can have a triangular pyramid (tetrahedron), a rectangular one, a pentagonal one, and so on. Similarly, you can have a triangular prism, a rectangular prism, and so on.