This framework is based on a 3 frequency icosahedron geodesic sphere with a 5/9 truncation.
A 3 frequency dome of this type has 3 strut lengths which form 2 triangle sizes. When properly assembled, the 30 "A" stuts, 55 "B" struts, and 80 "C" struts make 30 "AAB" and 75 "CCB" triangles. These 105 triangles form 5/9 of a complete sphere.
The chord factors to calculate the strut lengths are:
A=0.348615
B=0.403548
C=0.412411
These numbers are multiplied times the radius of your dome to get the length of the struts. This design is optimised to get 3 struts from a standard 10 foot length of conduit, requiring 55 pipes or 550 feet for the complete dome. A radius of 7 feet 10 and 9/16 inches, or a diameter of 15 feet 9 and 1/8 inches, is needed. It is really a shame that pipe doesn't come in metric lengths in the USA since that would simplify the calculations.
| chord factor | radius | length in feet | length in inches | cut length | |
| a | 0.348615 | 7.88 | 2.75 | 32.97 | 33.97 |
| b | 0.403548 | 7.88 | 3.18 | 38.16 | 39.16 |
| c | 0.412411 | 7.88 | 3.25 | 39.00 | 40.00 |
Carefully measure and cut the 30 "A" struts, the 65 "B" struts, and the 80 "C" struts to the "Cut Length" shown above, being as accurate as possible in your measurements. If you cut three "C" struts from a 10 foot pipe, you will have no leftover since 3 times 40 inches is 120 inches or 10 feet. The "B" struts are slighty shorter so you will have about 2 1/2 inches of leftover when cutting 3 "B" struts. 3 "A" struts will leave about 20 inches of leftover. Thus, while the dome only uses 517 feet of pipe, you will need to buy 550 feet of pipe. In this design, 1/2 inch electrical conduit is used. For a larger dome you would use larger pipe for more strength.
If you have access to scrap or salvaged pipe you would probably want to adjust the radius of your dome to optimize the pipe you have available.
You may have noticed that the cut length is 1 inch longer than the strut length. This is so that you can drill a hole 1/2 inch from each end of the pipe, and when the struts are bolted together the bolts will be the right strut length apart. Since the pipe is 1/2 inch in diameter, 6 of them bolted together would need over a 3 inch bolt, and would not give a very strong joint. For this reason, the ends of the pipe will be crushed to make a flat thin area to be bolted to the other pipes. Many people crush the pipe by hitting it with a hammer. This is an effective and cheap method. A mechanical pipe crusher can easily be made from scrap metal, like automobile springs or heavy steel bars. When crushing electrical conduit it is important to turn the seam to about halfway between the top and the side of the pipe so that it will not split when the pipe is crushed.
After crushing, the bolt area of the pipe is about one 1/8 of an inch thick, so 6 of them would be around 3/4 of an inch thick when bolted. For ease of assembly, a bolt at least twice that long, or 1 1/2 inches, is used. A washer under the nut is recommended to make the nut easier to tighten. This design calls for 3/16" or 1/4" bolts.
This is the pattern for assembling the studs. You can start at the center which is the top of the dome, or at the outside which is the bottom. Starting at the bottom will eliminate lifting the dome as you add struts, but will require ladders or scaffolding to place the highest struts. If you start at the top you can lift the edges as you add struts to the bottom and do all your work from the ground. You will probably need one to two helpers for this method. Another way that has been successfully used is to start at the top but build the done upside down, then roll it over. This method greatly stresses the ends of the struts, and will rapidly fatigue the metal, so should not be used many times. The finished frame is not heavy and can be moved relatively easily by two or more people.
The finished frame is strong enough to be climbed on as long as all of the weight is put at the hub. Half inch conduit is not strong enough to take much weight in the middle of a span.