Best way to sand and finish Polyethylene

[Linus Knives]

I'm workin on rehandling this case knife but my sandpaper doesn't seem to want to polish this up. Any ideas? It looks about like this now and I want it to look like the second picture...
I have done more shaping to the handle but it doesn't hog easily at all and only does with a new 36 grit belt.
Im using a block of plastic (Polyethylene) from amazon which is about the same as what's in the picture.

 

[midnight soda]

PE is a thermoplastic, so you can heat it up after sanding and buffing, if you're after a shiny surface. I'd probably go to roughly 1200 grit before buffing with a fine cut compound, but it works just fine with a coarser grit, if you're patient on the wheel. I usually overshoot my grits, so I can keep my pins and/or spine flush on the wheel.

Edit: if you still have some of the material left, it's always a good idea to check on a separate piece what sort of finish would look best for your application.