You can buy a foam cutter for thick styrofoam here: http://www.uline.com/BL_505/Foam-Hot-Knife?pricode=WO230&gclid=CP_EwaKiwKACFYk55wod0HpzUQ
White, thick plastic foam, very light, used for fruit boxes and packing.
Well, you could try those Styrofoam "chips" used as packaging in shipping and strips/squares of bubble wrap.
You basically need a hot wire. There is lots of info available on Google. Here is one URL with instructions for a home made foam cutter. http://www.instructables.com/id/Hot-wire-foam-cutter
A CNC foam cutter could probably cut any soft material, since the heated wire would likely be able to slice through it.
it has to heat up so it cuts the foam.
To effectively cut styrofoam blocks, you can use a sharp knife or a hot wire cutter. Make sure to measure and mark the cutting line before cutting, and apply gentle pressure to avoid crushing the foam. Be cautious and work in a well-ventilated area when using a hot wire cutter to prevent fumes.
The term is "styrofoam" (originally a trademark for expanded polyurethane foam).
aerogel and styrofoam
Expanded polystyrene (EPS) foam is similar to Styrofoam in terms of its lightweight and insulating properties. Other materials that are comparable include extruded polystyrene (XPS) foam and polyurethane foam.
To effectively cut styrofoam, use a sharp knife or hot wire cutter for clean edges. Measure and mark the foam before cutting, and make slow, steady cuts to avoid jagged edges. Wear safety goggles and work in a well-ventilated area when cutting styrofoam.
Expanded polystyrene foam.
The trademarked name "Styrofoam" (extruded polystyrene foam) has become so generic a term that it is almost never capitalized.