Contractible edges in 3-connected graphs

By Tutte's constructive characterization of 3-connected graphs (Indag. Math. 23 (1961), 441–455), we see that every 3-connected graph of order at least five has an edge whose contraction results in a 3-connected graph. We call such an edge a contractible edge and study the distribution of contractible edges in 3-connected graphs. As a consequence, we prove that every 3-connected graph of order at least five has [|G|2] or more contractible edges and determine the graphs which attain the equality.