Tools and materials I propose:
This is a classic woodworking puzzle. I thought it would be a nice paradox to transfer this idea on the lathe. That's because the lathe usually produces round objects!
First of all I used my Jointer/planer and the table saw to create a wooden cube out of iroko wood.
I then marked the centers on each side of the cube. 
I mounted the cube on the lathe using flat jaws on the chuck. I usually use these jaws for cleaning bowl bottoms. 
On the tail stock I placed a drill chuck with a forstner bit. The lathe was set at it’s lowest speed, around 500rpm.
Then I drilled each side of the cube little by little. I kept on drilling further and further on each side. 
At some point inside of the bigger cube you get a smaller one.
It is a really interesting experiment! I hope you liked it.
See you soon with a new project video!
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