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Important safety notice. Please do not build hexayurts out of any flammable material. This goes double for foam! 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.
Although free-standing foam may not burn well, an enclosure made of foam can burn catastrophically. The foam traps the heat, reflecting it back to the fire and quickly igniting the entire building. According to this article, temperatures can reach 10,000 degrees and buildings have literally been blown apart by the sheer force of the flames. Warehouse-sized buildings can be fully engulfed in under five minutes. The article is about urethane foam, but polyisocyanurate will probably behave similarly. http://static.monolithic.com/foam/fire_hazard/index.html
Here is some video of a sheet of R-MAX (which is very similar to Tuff-R) being set on fire. As expected, it does not burn well in open air. However, this should not give a false sense of security about foam-lined buildings. Foam manufacturers used to think their foam was "self-extinguishing" - but in an enclosed space, it is not.
(shot by Arthur Zwern of http://progressivebuildingsolutions.com)
In addition, 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.
http://groups.google.com/group/hexayurt/browse_thread/thread/99fbdd6cf9ddaca8 has pictures of the test conducted by Spiral which revealed this problem. Thanks, Spiral!
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. Please, put in the extra work and source the safest possible materials. This is your responsibility.