First, here's the animation for truncation (You may have to click on the image to see it).

And here's cantellation.

I wanted to do this for bitruncation and cantitruncation too, but I can't seem to find a well-defined definition of either, other then 'truncation beyond rectification' and 'truncating its rectification'. Can someone explain the definitions of them to me, and other types of truncation in general? Thanks!