Thanks John, I always smile when I see patterns with an out-of-phase lobe described as cottage-loaf. It's an apt description even if I've never seen an actual English cottage loaf.
I ask the questions above because I'm curious about the performance of stereo arrays that are combinations of these individual microphone polar patterns. I have a feel for what happens and why, developed simply from trying things and thinking about it, but I have no real theoretical basis for what Todd R, Freelunch & I are suggesting in our posts above. I may be making some incorrect assumptions, but this is how my thinking goes:
As a simplification, lets assume two cardioid mics and forget about worrying about an appropriate stereo recording angle. If I place those mics coincident and pointing 180 degrees apart, the result should be an equal pickup of sound in all (horizontal) directions around the mic array when considering the sum of the stereo information, not each mic individually. If instead I point them in the same direction, the sum of the stereo information will favor sound from the direction in which they are pointed and suppress sound arriving directly from the rear, to the greatest extent possible using the cardioid pattern. Obviously there is no real stereo information in that case because the mics are coincident and pointing the same direction, but we're ignoring the recording angle at this point.
Those two configurations are the extreme positions along the X/Y angle continuum for coincident cardioids. I probably wouldn't choose either but instead choose something in between, and choosing an angle in between would mean that the total direct sound pickup of the stereo array would also fall somewhere between that of the extremes.
If I then want to keep that maximum forward directional coefficient of the stereo array, but actually record stereo information, I can keep the two cardioid patterns pointing directly ahead, but separate them so that they act like A-B spaced omnis using time of arrival differences to produce stereo. They should then continue to maximally reject direct sound arriving from the rear of the array and also produce A-B time-based stereo.
If I'm willing to trade some of that maximal rear rejection for other attributes, I can adjust the angle between microphones angles against the spacing between them to: 1) adjust my desired recording angle, 2) change the balance of time-difference vs level-difference stereo, 3) adjust how much direct sound arriving from the front is favored over direct sound arriving from the back, within the limits of the directional coefficient of the cardioid pattern. I make that adjustment with the understanding that all three are inter-related so I'm changing all three of those things at the same time.
Extending that line of thought to other microphone polar patterns is somewhat more complicated, and is where I start to wonder if my empirical based understanding begins to break down. Trying to paint a mental visual image of the averaged stereo-sum pattern of two cottage-loaf microphones positioned at various angles starts to exceed my mental imaging abilities. I'd think that supercardioids (for example) would behave in a way similar to the example I made above using cardioids, within the limits of the individual polar pattern of the mics as outlined in your post, but perhaps I'm missing something.