parallelogram division

is there any way to divide the surface to a subsurfaces that its cells are similar to the attached image , a parallelogram division ,

dividing surface using the typical approch is according to U and Vs of surface therefore giving rectangular or square division but  what i want is parallelogram subsurfaces (lunch box doesn't havewhat i want )

i Tried many approachs without reaching any results , I tried  to shift the points of "divide surface' component also i tried to map curves using map to surface approach  , but it's not practical approach ..

thank you for your help 

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