  The $3$-polytopes are planar, $3$-connected graphs. A classical question is,
for $r\geq 3$, is the $2(r-1)$-gonal prism $K_2\times C_{2(r-1)}$ the unique
$3$-polytope of graph radius $r$ and smallest size? Under some extra
assumptions, we answer this question in the positive.
