Why does halite have perfect cleavage at the (110) plane?
I think the commenters have identified the issue. Halite does not have perfect cleavage along the {110} plane. As recorded in Mindat, Halite has perfect cleavage alone {100}, {010}, and {001}. This makes sense, as Halite is a cubic mineral (fcc), these are the planes you would expect it to cleave on.