I made this puzzle using the nechronius YouTube tutorial series keeping fairly close to the script.

First I drew a freehand diagram of the core to get my mind on the right track.


The core was quite easy to cut with a junior hacksaw. I kept the core assembled, turned a layer by 45 degrees and made the cut. I did damage one or two of the remaining faces as you can see on the top left cubie. The four marked cubies were glued after the core was filled.


The across flats measurement was 30mm - the same as the uncut core size.


But the widest point was 32mm. The outer pieces of the puzzle must clear this 32mm. I have seen one core rounded at the widest points to get a 30mm clearance.


Using a 12V multipurpose hand tool with a drum sander I sanded out these arcs which make up a circle of just over 32mm diameter in the edges of the 2x2x3...


...and  these cutouts on the corner pieces. They look like compound curves but each corner just has two separate planar cuts.


The core was bandaged just prior to this next step - ie the four pieces marked above were glued together.
This is the key stage of assembly where the position and squareness of the edge pieces is attained (or not quite so in my case - the end was in sight and I was too impatient).


Now the edge pieces are attached and I'm wishing I'd been more careful.


Three of the corners didn't glue on at the first attempt. Again hasty botching meant the puzzle looks disappointing.


I've just used these quick stickers to experience the working puzzle, but I haven't reinforced the pieces so one corner came apart after a few solves.
I intend to make another Slim Tower using my own method of aligning the pieces.