Flying saucer. and a cone
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a pentagonal pyramid
base
If you mean a pyramid with a four sided base, it is a square pyramid. If you mean one with four faces, it is a tetrahedron.
No. Polyhedra are three-dimensional objects, and the base of any prism, strictly speaking, should be two-dimensional. Any convex polygon (which is two-dimensional) can form the base of a pyramid. A circle, which is technically not a polygon, is the only convex two-dimensional figure that cannot form the base of a pyramid because it forms the base of a cone.
pyramid