An antiprism is a polyhedron consisting of two parallel copies of some polygon, connected by an alternating band of triangles.
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A pentagonal antiprism.
A prism is a polyhedron comprising two parallel polygons (bases) joined together by a set of quadrilaterals. In an antiprism, the two bases are twisted in respect of one another, and they are joined together by a series of triangles pointing in alternating direction.
There is no special name. In a prism it would be a quadrilateral, in an antiprism, a triangle.
It depends on the shape. The top of a pyramid will be a point (the apex). The top (and bottom) of a prism or an antiprism will be congruent polygons.
It could be a prism, but need not be. A regular dodecahedron, for example, is not a prism but has parallel and congruent pentagonal bases. You can also have any antiprism (see link).