12mm is half inch; LDPE is not going to be very rigid in larger sizes. I'd guess you'd want about 3/4", and may still beed bracing to get rigidity.
Also, PE is a fairly low energy plastic, so gluing stuff to it (or gluing it together) is damn near impossible (though there are a couple of epoxies that will work with a little prep steps.) On the up side, it cuts and machines pretty well, and takes and hold screws decently.
Lastly, PE tends to be fairly heavy for a given volume.