what is the chemicl equaion with this brilliant reaction (one large drop will dissolve a large hole through a 2cm block of polystrene!)

There is no chemical reaction. It is simply the polystyrene dissolving in the DCM. DCM (dichloromethane) is a very solvating organic solvent (i.e. it dissolves a lot of things very well). The majority of block polystyrene is actually only air, there is very little that is actually polymer fibers.

 

So simply, the polymer is dissolving in the DCM.

so te gas that bubbles off is air then?

More than likely yes, it is simply the air that is trapped in the polymer mesh being released as the polymer dissolves.

The polystyrene foam is made with another gas first... often it's pentane. The mixture gets extruded. The pentane evaporates when the pressure drops to atmospheric, and it makes the foam expand. Then the newly produced foam is then left to "breathe"... and the pentane gets replaced by air.

 

So in ordinary polystyrene foam, the pockets are filled with normal air by the time it is used for any packaging.