Our first natural building project, Snail Cabin, has a reciprocal frame roof inspired by the spiral of a snail’s shell. This is a type of roof in which three or more beams provide mutual support, avoiding the need for a main beam that crosses the house, or a central post.
It’s a self-supporting structure, in which each beam rests on the previous one, and the last beam fits underneath the first one. While building it you need to support the first beam temporarily; when the support is removed the whole structure should neatly lock together.
Reciprocal frame roofs are beautiful and strong but rather fiddly to build — especially when it comes to cladding the roof structure with boards.
We liked the finished structure so much that we went on to build a smaller reciprocal as a cupola over the top of the first, to make a double reciprocal frame roof.
To calculate the dimensions for the beams we used this reciprocal roof spreadsheet, which covers both the specific case of a round building where all the beams are the same length, and the general case of a non-round building (like Snail Cabin) where they are not all the same length.
NB. The hyperlink in the original spreadsheet is no longer available. However a cached version is available here: https://web.archive.org/web/20081205161402/http://www.mts.net/~sabanski/pavilion/