Inside out turning starts with a glue up of four sticks cut perfectly square and glued together to make a square twice the size of the cut pieces.
There are limits to how deep a cut can be made and not have the turning ruined because the cut was too deep. One inch square pieces will be glued up to create a two inch blank in this case. When the blank is mounted in the lathe the first order of business is to turn the area where the window is to appear to the max diameter which in this case is two inch diameter or a one inch radius as seen on the right. On the left is what it would look line if it was turned inside out now. The center diamond would be air space and the points of the diamond are where the windows will appear when more turning is done. This shows that a one inch deep cut measured from the corners would be too far. The maximum cut has to be at least one eighth inch short of one inch and that may be pushing it. So if two inch sticks are glued up to make a four inch square the cuts have to be less than two inches deep measured from the corner. Depth of cut mystery solved.
Okay, time to get the table saw tuned up to cut perfect square and install a smooth cutting blade. Start by cutting four sticks the same length and perfect square. I used one inch square by six long pieces here.
Decide the best looking orientation of the end grain and put a rubber band around them. Mark the four inside corners and number the pieces.
Keeping the same orientation turn the inside corners to the outside and glue them together. A quarter inch line of glue on the ends is about all that is necessary as they will need to be split apart later.
Let it dry and wrap the ends with tape. Heavy plastic tape can be as an added insurance that the blank will stay together. The tape is also a reminder to not turn that area away. It needs to remain for gluing later.