Maya Modeling :: Tool Similar To Max Edge Turn?

I know that you can spin edges (that are visible).  And I know that you can view "face triangles" (to view otherwise "invisible" edges.)But I cannot seem to select these "face triangle edges" or manipulate them.  I can create a physical edge, yes, and place it where I want, but if I remove the edge, then maya seems to revert to its own random placement for the "invisible face edge."  So, I feel like I have no control over the bend of non-planer quads. 
 
In max, when you are working with edges, there is a tool called "turn."  When selected, it reveals all hidden edges, and allows you to spin them to the angle you want.  Turn off the tool and the selected edge position remains.Can this be done in Maya?  And even if you cannot do this, is there any way to control the position of "invisible edges" in maya?  Something like a "spin quad?"