Reverberation equations fail in extreme geometries where surfaces are visited unequally

Evidence

However, one must be careful in taking this result to extremes. A long and very thin cylinder will have a large surface area, but Equation 6.6 will not predict the reverberation level correctly because in this case, the sound will not visit all the surfaces with equal probability. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1772

Categorization

• QUESTION: What geometry conditions ensure sound visits all surfaces with roughly equal probability? The text gestures at the assumption without stating the threshold.
• XREF: connects to: Extreme room shapes break reverberation-field formulas because sound visits surfaces unevenly — David Howard, Jamie Angus, coustics and Psychoacoustics, 1811