OK, I believe that you know what he's talking about. However, his concerns about the observation angle are valid, and the number of facets really don't play into it -- it wasn't really the right thing to bring up at that point.

Let's suppose that bicycle reflectors reflect incoming light back in a 3 degree cone line you said. Let's say exactly a three degree cone -- no more -- just to make things simple for this example. Let's say the light and eye are 6' feet away from each other, and 100' away from the reflector. 100' * sin(3 degrees) = 5.3 feet, which is less than 6', so the reflector will not reflect *any* light back to the eye, no matter how the facets are aligned or how many there are.

Now, that's not a real world situation, as the three degree thing isn't a strict cutoff, it's more where the intensity starts going way down. In the real world, you'd still see the reflector, just not very well. (I'll ignore any reflections due to it's mirror-like covering (only works at one specific angle) and any reflected light simply due to it being a red object -- as that's really dim compared to the retroreflector reflection if the observation angle is low.)

And of course, 5.3 feet is pretty close to 6 feet. If it's too close for your example, say the cyclist is 50 feet away -- then we're talking about 2.6 feet vs. 6 feet, and it barely works as a retroreflector at all. Of course, by that point the headlights should be illuminating the entire bike pretty well, not just the reflectors.

But certainly, the multiple facets aren't there to make the observation angle larger -- they're there to make the range of entrance angles where it works well larger. The wikipedia article I gave earlier does mention the two angles, though it may not really explain the difference very well.