Not quite. Those line segments are the lines which are the edges of the faces.
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pyramid
It is a corner: a point where three of more faces meet.
a prism is a polyhedron with two congruent faces, called bases, that lie in parallel planes. The other faces, called lateral faces, are parellelograms formed by connecting the corresponding vertices of the bases. the segments connecting the vertices are lateral edges. the altitude, or height, of a prism is the perpendicular distance between its bases.
The 3-d equivalent of a polygon is called a polyhedron. A polyhedron can have 4 or more faces. Cutting off a section of the polyhedron near a vertex adds another face. And it adds at least two more vertices (at least three new, but one lost), so you can keep adding faces.
A polyhedron with 9 faces: a nonahedron.A polyhedron with 9 faces: a nonahedron.A polyhedron with 9 faces: a nonahedron.A polyhedron with 9 faces: a nonahedron.