Wikipedia's Iridium_satellite constellation; In-orbit spares says that Iridium satellites have an inclination of 86.4°:
Significant orbital inclination changes are normally very fuel-intensive, but orbital perturbation analysis aids the process. The Earth's equatorial bulge causes the orbital right ascension of the ascending node (RAAN) to precess at a rate that depends mainly on the period and inclination. The Iridium satellites have an inclination of 86.4°, which places every satellite in a prograde (inclination < 90°) orbit. This causes their equator crossings to steadily precess westward.
A spare Iridium satellite in the lower storage orbit has a shorter period so its RAAN moves westward more quickly than the satellites in the standard orbit. Iridium simply waits until the desired RAAN (i.e., the desired orbital plane) is reached and then raises the spare satellite to the standard altitude, fixing its orbital plane with respect to the constellation. Although this saves substantial amounts of fuel, it can be a time-consuming process.
Question: This replacement scheme would work at other high inclinations, and polar coverage could still (probably) be 100% anywhere between 75° and 105° (they're spaced every 30° at the equator). I can't figure out anything profoundly special about 86.4°. Not that there needs to be. Was this a complex yet uninteresting optimization of several things, or does this particular inclination angle reflect something specific and significant?
For more about the constellation see the excellent answers to What (actually) makes Iridium “the world's only truly global mobile satellite communications company”?