Digital Ice Cubes Problem

I have been trying to get into 3D a little bit here and am still very new at this. I rendered these ice cubes last night using LightWave 3D:

ICE CUBES

and cannot figure out for the life of me why the cubes have the lines in the cube and in the shadow. I thought at first it my be the ray recursion limit so I manipulated that from 4 to 16 with the same results. Any ideas what could be causing this?