Hi Wayne
The inside of the brass lap is tapered on both ends, both ends are internally threaded, same thread both ends.  The driving shank is fitted up just like a bbl into an action.  The other end has flats ground on the external portion, then threads, then a taper to fit the internal taper of the lap. Once snugged up the lap expands quickly, that is why you need a feel to what you are doing, or you can ruin the brass lap in a hurry.
This lap will only work on the neck portion of a die.
Htp  ld1
My laps are through hole, I just checked on e-bay and they had some blind hole laps also, they had a allen head screw to expand them.