Math Series #9

[A prism is a polyhedron comprising an n-sided polygonal base, a second base which is a translated copy of the first, and n other faces joining corresponding sides of the two bases. All cross-sections parallel to the bases are translations of the bases.]

The vertices of a prism are divided into $2$ equal parts for $2$ polygons. So each of the polygon has $v/2$ ( $v=$ number of vertices) edges. Then the vertices of polygons are connected one to one. From this we get $v/2$ edges (equal to the number of vertices of each polygon).
So total number of edges $=v/2+v/2+v/2=3*v/2=e$ ( $e=$ number of edges)
Now, $3*v/2=e$
$=>v=2*e/3=2*342/3=228$