weld 3 pieces of rebar, steel rods, even pipe at 120 degrees apart it should then resemble a pyramid of 3 sides.. then weld a pin or plate on the apex of the 3 pieces to clamp in a regular vise. the 3 rods should be covered with clear poly tubing or rubber hose. such prevents marring the helmet.
not seeing size of the helmet, id guess the 3 pcs welded together should each be about 12" long. you'll find the 3 legs form a triangle of sorts. this will allow positioning of the helmet in just about any orientation.
i have made several different sizes for carving odd shaped rocks, or just about anything else one would want to work on. again, no special vise needed, most any will work that can support whatever tapping , engraving, etc that you want to do.
the shape would roughly resemble an upside down umbrella with just 3 rods sticking up., with the vise plate or pin on the bottom. the actual degree need not be exactly 120, but if reasonably close, will work. this idea could also be done using wood. i simply find welding the steel much quicker than fiddling with wood
the foto speaks better than all my words