I truly appreciate your informative and highly detailed response. For 
helping understand spherical harmonics (or Legendre polynomials?), and 
for mics lying on surface of a sphere, this helps a lot.

But here's what
 I don't understand about the quaud (quaud.io) mic: They say the four 
omnidirectional mics lie on the corners of a tetrahedron--essentially 
same arrangement as Soundfield, but with omni mics and 
positioned on corners of tetrahedron. Re mics on a sphere: In a corner-oriented 
tetrahedral arrangement, the mics would lie on a *virtual* sphere just as much 
as mics on a sphere could be lying on a virtual tetrahedron. But at some point 
the actual (physical) surface becomes a piece of the whole. This is clearly 
evident when the sphere is large enough to be a human head. So I'm not always 
clear as to whether it's the mics' virtual orientation in space, or the 
physical boundary of a spherical surface, that *shapes* the sound and creates 
the requisite time and pressure differentials.
Dave M's original post states that someone else is... again... re-inventing the 
Soundfield mic. I'm sure that I'm not the only person who is curious as to what 
makes the quaud (Trademark) mic *unique* and different from the Soundfield 
mic--particularly if the quaud mic is patented. Is, for example, more than one 
tetrahedral arrangement used to achieve *surround* spacing--which would then
 be a wholly different thing? I need to read further. Thanks again for 
info. The following was cut-and-pasted from their website (I think Dave 
provided all of this in his post, too):

quaudio
 comprises four omnidirectional microphones located at or near to the 
corners of a regular tetrahedron. Since these capsules are
 omnidirectional they can be located at the opposite corners of a cube 
with no loss in generality. This arrangement is straightforward to 
achieve in a standard PCB assembly line by soldering two pairs of MEMS 
or electret capsules on opposite sides of the substrate. Alternatively 
it is possible to solder three capsules to one side and a single capsule
 to the other. In both cases the acoustic centre of each sensor should 
be separated laterally by a distance corresponding to the vertical 
separation between membranes on either side of the device
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