Note that if $m_{j}=2$ for all $j=1,\dots,8$ then $n=0$ by (4.1) and the bundle $P$ extends over every puncture: in fact $P$ is a $4$–torus and our construction reduces to the usual Kummer construction along a family of $4$–tori collapsing to a $3$–dimensional torus. This is the case considered by Page in [37].