This hot wire cutter uses resistance wire from Maplins (order code BL64U). the wire is stretched between two arms and tensioned using elastic bands. The wire is actually quite low in resistance - so you need a low voltage transformer to supply it - I found 2 Volts works quite well for about 6“ of wire - you need the wire hot enough to melt the plastic - but not so hot as to glow and burn out. I used an old Toroidal transformer and re-wound it for 2 Volts. Toroidal transformers make it really easy to add your own secondary winding and adjust the number of turns and therefore the voltage.

A foot switch is a really good idea as it allows you to control the cutter power - and give you both hand free to move the piece and/or cutter.

Of course for safety there should be a cover over the mains connector block.

To get nice straight cuts - use metal strips (I use the backs of hacksaw blades) taped or pinned to both sides of the polystyrene - then run the cutter wire through the part so it is lightly tensioned against both strips.