Styrofoam (aka expanded polystyrene foam in the UK) is widely used in model making and domestic crafts. When it comes to carving it into the desired shape with a knife you quickly become surrounded by little white beads with a static charge that makes them stick to everything. It’s better to use a hot-wire cutter, which improves cutting accuracy and leaves no mess to clear up. For consistent results the hot-wire temperature should be adjustable — sounds like an ideal application for a phase-angle power controller.