I got Accepted using this approach
divide three euler angle into 50 pieces each of them is 2*pi/50;enum each euler angles and
compute minmimum max different of distance to three faces.
for(alpha=0;alpha<=2*pi;alpha+=dtheta)
{
if(min_dist>compute(alpha))
{
min_dist=compute(alpha);
ch=alpha;
}
}
low=ch-dtheta;
high=ch+dtheta;
then ternary search [low,high]..
Do you understand?