I bought this for my wife and would like to be able to tell her what the name of this is.
The top part is Astrophytum myriostigma. I don't know what it is grafted on. In the spring, you could cut off the Astro, and grow it on its own roots, if you like. It likes a lot of sun, and very dry conditions.
I think it's grafted on Harrisia jusbertii.
I like it.Whatever it is!