calculation of pcs
I have thought about this same thing. The argument is that the band extremes almost always occurs at the key points of symmetry. So if you want to calculate the width of a photonic band gap, checking the key points of symmetry will give you the right answer 99.99% of the time and is much faster than calculating every point in the irreducible Brillouin zone.
But you are asking about the 0.01% of the time and an explanation of what is happening. Qualitatively, as your wave "looks" in any particular direction, it sees a Bragg grating. Each direction through the lattice has a slightly different Bragg grating. Imagine a lattice constructed of an array of spheres. There is a smooth and consistent transition from "Bragg grating" to "Bragg grating" as you scan directions through the lattice. This ensures no surprises in terms of how the band gaps shift around. The shortest and longest period gratings will always occur in the directions you would expect. This same geometrical argument holds for most shapes your lattice may be composed of.
I suppose if your lattice were composed of something oddly shaped (maybe like a donut or snowman), it could effectively produce additional Bragg planes in your lattice, above and beyond what that lattice itself would give you by default. I "think" perhaps this would give you a lattice where a band extreme could fall somewhere other than a key point of symmetry.
This could, perhaps, make an interesting paper. I know there is some interest in indirect photon transitions and this could play a role in that.
If you are looking for more on photonic band diagrams and qualitative descriptions of this kind of thing, you might be interested in chapter 2 of my dissertation. You can download for free from here:
**broken link removed**
Hope this helps!
-Tip