Hi Antonino - yes I see that is a bit odd.

The problem here is that if you have a solid base object, the booleans will tend to expect either a solid cutting object, or for a surface one that fully divides the solid into 2 smaller solids.

In a sense the booleans will try to generate a solid as the result if the original object was a solid.

If you want to cut out a piece of a solid like you are showing there, you should use the Edit/Trim tool for that type of cut instead. Trim does not attempt to keep solids as solids and will let you cut up the outside skin of a solid any way you want.

It may be easier for you to use Edit/Separate on the solid to break it into 6 individual surfaces first, and then work on those surfaces separately. You can then later on use Edit/Join to glue them back together into a connected object after you are done editing the pieces.

Also instead of using a plane as the cutting object, I'd recommend using a rectangle curve as the cutter instead. Coincident surfaces tends to be a more difficult calculation and also it can be more difficult to select by clicking when there are 2 coincident surfaces. Curves are much easier to select, so it is more of a recommended workflow to use a curve as the cutting object in this case.

- Michael