The three dimensional counterpart of a polygon is called a polyhedron.  A polyhedron is formed when you join the polygonal regions (called faces) at their sides (called edges).  The faces intersect at the edges only, with each face intersecting exactly one other face at each edge.  The vertices of the polygons bounding the faces are the vertices of the polyhedron.  You can think of a polyhedron as a figure that seperates space into two distinct parts, an interior space, and an exterior space.

    Below is a diagram of a polyhedron and the terms used to represent is parts.

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