Important safety notice. Please do not build hexayurts out of any flammable material. In the past, people have built them from non-fire rated materials including polyisocyanurate insulation (Tuff-R from Dow, often sold at Home Depot.) I do not regard that as safe if the building is exposed to sources of ignition like open flame, or mains electrical devices. Any non-fire rated substance should not be used for camping, and is generally suitable only for demonstration purposes.
Now, all that said, here is some video of a sheet of R-MAX (which is very similar to Tuff-R) being set on fire.
http://www.youtube.com/view_play_list?p=36DB80EAF1D4161B
(shot by Arthur Zwern of http://progressivebuildingsolutions.com)
As you can see, the material is reluctant to ignite, and when it burns, it burns very slowly. We're fairly sure the smoke is very toxic, so there is still cause for concern about fire issues, but the risk does not appear to be that the entire building will go up like a bonfire immolating everybody in it. It's possible that with a couple of smoke detectors of different brands mounted in the Hexayurt, no sources of ignition inside the building and a generally careful attitude, the risks from fire would be within an acceptable tolerance for any given use.
However, bidirectional filament tape has turned out to be very flammable, and burns hot enough to ignite Tuff-R type insulation. This is a "negative synergy" - the two materials together are more of a fire risk than either alone, because the fast-burning tape can ignite the boards. We highly recommend covering all exposed filament tape with foil tape, which is a few dollars a roll at Home Depot and similar places.
Estimation of fire risk for any given situation is a decision that only the person building the hexayurt can make. I recommend you watch the video, get a clear sense of what's going on, and make your own judgments. All we do is make the information available, and you make the decision.
Good luck, and enjoy your Burn.