If the helmet, is in fact polystyrene, or a thermo-plastic like ABS or PETG, then a solvent cement is the ideal material for the repair. "Weld-On" is one brand, of this type of cement.
All the above suggestions are a dissimilar glues, which, with proper surface prep, may work. Although I would avoid cyanoacrylate adhesives, as most of them will embrittle styrene.
Solvent cements are specifically engineered for each thermal plastics, and come in different types, depending on your type of plastic. (Acriylic, ABS, PVC, Styrene, PETG, Kydex....) These are most common in clear, but ABS & PVC cements are available in black.
These solvent cements will melt the base material, and once the solvent in them has evaporated, you are left with the same base material, in this case styrene. Note; solvent cements only work on thermal-plastics, and will not work on thermal-set plastics, Epoxy, polyurethanes and so on.
The best and most stable way to repair a crack like this, is to get a thin piece of the same plastic, .030" (1/32") and fabricate a patch, which is a plate, that can be bonded to the inside of the helmet. It should be 1/4-1/2" bigger than the crack. If the area to be repaired is on a compound curve, then use a heat gun to soften the patch and form it to the inside area over the crack. Use masking tape on the outside, to hold the split area together, and keep the surfaces lined up and flush.
Solvent cements come generally in 2-3 "thicknesses" (viscosities).The thicker versions have dissolved quantities of the base plastic in them.
The water thin versions of the solvents should only be used when you have 2 surfaces perfectly matched and held snug (like the seams of a display case).
For this repair, I'd use the ticker version of the solvent. BUT! do not use too much, as the solvent with melt both the helmet and your patch and if you use a big glob of the solvent cement, it can soften the thin material of the helmet enough to distort it. Since these cements contain solvent, which evaporates quickly, you want a nice match to you patch, and the inside of the helmet, and a way to clamp the pieces together, or a weight that can keep the patch in contact with the helmet. This can be something as simple as a plastic bag fill with sand (lead shot is better) If the patch fits nicely, and doesn't move around easily, you can also just hold it by hand.
Apply the solvent to both pieces, and quickly apply you patch over the crack.
Once the solvent has evaporated, the helmet has been repaired with, styrene. So it should not split again, even with temperature changes and repeated flexing. Which may cause the other suggested repair methods to fail.