Step 3: Making the skull cap
First, I made a foam band with consistent 1" thickness. It's easiest to simply cut a strip off the edge of one of the thick EVA floor pads (and carefully removing the puzzle pieces at the edge). The more accurate, the better. Wrap the strip around the circumference of the cardboard tube, mark the intersection of the foam, and cut the excess off. Then wrap the foam back around and hot glue the edges together so the band fits snugly onto the tube. Tip: Add hot glue to both sides quickly, then press together. Gluing both sides of the foam makes the bond much stronger.
The top of the band will be glued to other pieces of foam, so it's best to leave the worse-looking side up and leave the cleaner edge down where it may improve the helm's final appearance. The band I made has two glue seams, as can be seen below. This isn't ideal, but I made it work by evenly spacing them out in reference to the glue seams on the rest of the skull cap. This is important because you will need to cover the seams with other pieces of foam, and by evenly spacing these out they can be strategically covered by thin foam that looks like trim rather than a randomly placed piece of foam.
Secondly, I cut pieces of the dome out into quarters. I had bad luck attempting to thermoform pieces any bigger than this, so this is the largest I will recommend if you're using my method. Using a measuring tape, measure a quarter of the circumference of your cardboard tube. This distance should be roughly the same as the arc length from the top edge of the tube to the center of the half-spherical frame. Add at least 2-3 inches to your measurement, and cut out a foam square with that dimension. The more you add to it, the easier it is to form.
Thermoforming the foam is pretty straight forward, but you must take caution to avoid injuring yourself and burning the foam. I was able to thermoform my foam by preheating my oven to 350, putting the foam piece on the center rack, and allowing it to sit for around 10 - 15 seconds. The foam should be very pliable, but not smoking heavily. I wasn't able to avoid producing a little white smoke, so make sure you have a ventilation fan going above the oven if it happens and avoid breathing any smoke.
Quickly remove the foam from the oven ( I was able to touch it with bare hands, but it would be smart to have an oven mitt handy) and drape it over three of the semi-circular cardboard frame pieces, textured-side down . Press down on the foam at the top firmly, and press against the bottom edge to try to form a consistent circular part. Hold the foam stable for around a minute, and blow on it to help cool it off. This may take a couple of tries, but if you get one wrong, you can usually re-heat it and form it again or do touch-ups with a heat gun.
Using the cardboard imprints on the underside of the foam piece, draw an outline as shown in the image above, and carefully cut it out with a hot knife or sharp hobby knife.
Repeat three more times to make four quarters of your half-sphere. Place them all over the frame with the band to check the alignment and see if any additional trimming or forming needs to happen before gluing. When satisfied, glue them together with hot glue, while keeping them on the frame but avoid gluing the foam to the cardboard frame itself. Start by gluing your first piece to the top of the foam band, and glue small sections at a time until you glue the entire piece down. Using this method of slowly gluing small portions of the foam together, continue the process with the rest of the pieces until you end up with a finished skull cap as pictured.