This project has led me to two issues to be addressed: firstly, what solids can be made within the confines of a 2x2x2 or 3x3x3 mechanism that can be realized solely through truncation?
The second is the suggestion that, like the other puzzle forum(s), we have a subforum dedicated to math.
Your first question can't be answered without restricting truncations into specific patterns.
Without such restrictions truncating a corner by 9mm*10mm*11mm is something different compared with truncating a corner by 10mm*10mm*10mm. What restriction do you want to apply?
For questions about puzzle-related math there is the "General topics"-forum. I suspect that another forum will be ignored even more than that forum.
Regarding the shape:http://twistypuzzles.com/cgi-bin/puzzle.cgi?pkey=1853