Why is using a single phase device across phases of a 3 phase outlet OK?

My friend connected two wires to two "non-earth hole" in a 3 phase outlet (208V) to run a 220V single phase blower (Note: the outlet has four holes, one of them is earth). Basically, he used the potential difference of those two holes. I don't know why it is OK, so I used MATLAB to draw 4 curves (See picture)

Blue - regular sine wave 208V (peak is 208*sqrt(3)) where sqrt(3) is three phase peak ratio

Red - Same as Blue but with 2/3 pi shift

Green - The difference between Blue and Red

Black - regular sine wave 220V (peak is 220*sqrt(2)) where sqrt(2) is single phase peak ratio

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Officially, the green peak is >1.73 times the blue one. If the blower uses 220V single phase AC, then the blower should be connected to

----calculation process-----

Peak voltage of 220V AC = average voltage*single phase peak ratio = 220V*1.41 = 310.2V

Peak voltage of two legs out of three phase = (two legs potential difference from diagram)average voltagethree phase peak ratio = 1.73*average voltage*1.73 = 3*average three phase voltage

310.2/3 = 103.4V

-----end of calculation process----------

103.4V three phases power outlet (Two holes of a 3 phase outlet). Note: I understand that there is no such 103.4V three phase power outlet.

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Am I right?