Hexayurts are an incredibly simple, and affordable design to make a self supported fully enclosed building using common materials with a few simple cuts, and no material waste. If made out of plywood, they are animal proof, and if made out of insulation foam board, they are light and foldable. A Hexayurt has 6 sides, and with light materials, can be held together with tape. The link above shows how easy they are to make.
I've designed a variation called an OctaYurt because it has 8 sides. In addition to being substantially larger than a Hexayurt, it has a steeper initial roof pitch, allowing more headroom throughout. Here is a link to a google sketchup model. Using 8'x4' boards, an octayurt is 309 square feet. The core physics principles behind both hexayurts and octayurts is that the roof stays up as long as it has something pushing it in, and the connected outer ring provides that stability. The roof is resistant to too much force pushing it in because it reciprocates against the roof pieces next to it.
The easiest way to understand an octayurt is from the roof down. The roof is made with 8 isosceles triangles.4 are made by cutting an 8x4 along its long diagonal, and the other 4 are made by cutting an 8x2 along its diagonal. Here is what the roof looks like flat.
There are 3 levels to an octayurt. The 2nd level is made up of 4 8x4s attached to the large roof triangles, and 3 trapezoids attached to the smaller triangles. The trapezoids are made by cutting away a 4x2 triangle from each side of an 8x4, such that the trapezoid has a top side that is 4 wide, bottom side 8 wide, and height of 4. The reason there are 3 trapezoids instead of 4, is that one of the short sides of the roof is used for a door. Each section of the middle level is angled at 45*, and this causes the trapeze and rectangles to flush and reciprocate. On the door side, 2 middle level rectangles rest against shaped walls that act as a brace support.
The 3rd and last level is simply 7 8x4s stood vertically on their long sides on every side of the octagon except for the door side. The 6 2x4 triangles cut out to make trapezes, can be used to make an awning for the doorway.
Unlike the hexayurt, the octayurt does not have perfect math with these standard building materials. You can notice, on the south west corner, that there is an 8" "window" at the base of the top roof. This needs to be braced somehow. An approximate 27* angle will allow the top roof to be flush against each adjacent triangle, but a steeper angle for the large triangles allowing for narrow triangles to float on top a bit, and rest atop an extra strip of wood at its base that also spans between two large triangles in the roof. Another support strategy may be to use a steeper roof and have each adjacent triangle support the next, and ultimately supported by the door braces.
The Octiyurt is likely to require the same bracing techniques as the plywood hexayurt, and is too big to be practical as a festival tent replacement anyway. Uses include homeless and emergency shelters, but also retail kiosks, school and office space, and cabins in areas that allow temporary buildings without a building permit. The plywood hexayurt techniques still allow the building to be fairly easily dismantled by unscrewing braces.
If you have built a hexayurt before, you can reuse almost all of the parts for an octayurt.