I have plans to adquire a staco variac 6020-2P (manual) but I got confussed with the input connections.
From the manufactures manual the input connection is between terminal 1-4 (see attached figure).
I have a three phase wye electrical system at work (phase A,B,C Neutral and Earth). between any phase and neutral I have 120 V; and phase to phase I have 208 V.
Could I use phase A and phase B or any two phases to power the variac (connecting phase A to terminal 4 and phase B to terminal 1) or should I power the variac from phase to neutral (connecting phase A to terminal 4 and Neutral to terminal 1)

Please advice me how should I proceed or is all my Ideas are wrong, please tell me

 

For a three-phase input, the circuit shown is completely wrong in every aspect. Destruction of the Variac is assured. So the very first question is what do you need to achieve? A variable three-phase output? A variable single phase output? or something else? All of the three-phase variac installations that I have seen used three devices, connected in a WYE arrangement with what would be the #1 terminal connected to the common and the three #4 terminals connected to the three phases. The three slider connections were used as the three legs of the WYE connected output.

A "Delta" connection arrangement is also possible but it would have no good reference to the common, and so it would not be acceptable for many applications. You could connect them in a delta as you described, with the third phase being the junction between the #1 and #4 terminals, and the other phases being the two wipers, but it would only be useable with a Delta connected load.
Once again, the connections used depend on what you want to come up with. But the circuit posted is wrong for any application.