First off David, 180? is a phase shift.
Secondly, the same question remains posed to you that I posed with Beoseker. If this 180? view (i.e. perspective) was correct, then you should get the same results analyzing a non-symmetrical waveform as you are able to achieve with your symmetrical waveform.
Rick,
You are fixated on phase shifting. This is something that can be critical in the audio world but is not germane to the discussion here. You are so focused on dancing with alligators that you are forgetting the original objective was to drain the swamp (i.e. to get the voltages our loads need).
If you refer back to my Open-Wye to 3-phase 4-wire wire example, it shows you what we achieve by using waveforms that have a difference in phase. In that example, we used the difference in phase between voltages on either side of a winding (twice, in fact) to create the missing third phase. It was more pertinent than closing a delta because the open delta at least has the terminals available with the voltage we seek. The open wye does not even have the terminals we need so we must use the waveforms with the phase difference to get the third voltage. These phase differences are real and there are loads in the real world running on these derived voltages.
Shifting phases is not the same as a difference in phase. As for your symmetry fixation, what makes you think there has to be, or not be, symmetry in the waveforms when we are taking about supply voltages? You are too concerned about how the voltages are created instead of the result we seek: getting the waveforms we need to serve our loads. The way the voltages are derived may cause them to react differently when something happens on the supply side but how is that critical to our mission?
To put it in perspective, if we supply a three-phase load with a three-phase generator vs. a three-phase supply derived from an open-wye source vs. a three-phase supply derived from an open-delta source vs. a three-phase supply derived from a two-phase source, are you going to say that some of those three-phase supplies are not really in existence because they are just math anomalies? The truth of the matter is that the math is a model of the physical world and the physical fact is that the voltages from midpoint to the ends of the winding are different in phase. That is simply how voltages work and there is no universal reference we must use, and regardless of how many times you try to say it, it just ain't so.
Look at Bes's examples again and explain how you get the needed pulses if the difference in phase does not exist. Explain how a center-tapped full-wave rectifier with two diodes works if there is no phase difference between the end voltages. You must go back to voltage fundamentals and review what makes a voltage a voltage and you will recall that the choice of reference is just that: a choice.
I mentioned steady-state before and you did not follow why that was important. The importance is that our loads do not care about the very beginning and ending of signals (like might be important in audio). Those are the facts that we use to call things what we call them. All disciplines of electrical engineering are going to have their own sets of terms and rules and you are not going to find definitions for everything that will work everywhere.
