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.
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There is no special name. In a prism it would be a quadrilateral, in an antiprism, a triangle.
the difference between a cone and a prism is that a cone has no edges and only one vertex and a prism has both edges and vertexes.
A cube is a special kind of prism.
yes, they are different.
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).