No, but that leaves open the construction of a Half-Klein!
I suspect to acheive the 4D needed for construction without undesirable intersection, it will have to be implemented with a dynamic repeating 3D-Volume cycle, essentially rendering the 4D shape in time.
Much like time crystals.
A (nontrivial) 4D STM is all they needed. But.. that's "just" software "just" like
https://en.wikipedia.org/wiki/4D_scanning_transmission_elect...
(Not in the sense that "time" is involved but in the sense that what distinguishes 3D from 4D is just software . The same way you see 3D on your 2D screen)