Inspiration for the Machinism Dome originally came from http://desertdomes.com.
This excellent web page also contains detailed dome building instructions.

The building material used for the structure of the Machinism Dome is ³/₄" EMT pipe (conduit pipe). Long struts (l) are 10 ft (about 3 m) long, the short (s) ones are 8 ft 10¹/₄" (about 2.7 m). 35 l and 30 s struts are required.
The ends of pipes were flattened and ³/₈" holes were drilled about ³/₄" from the end of the pipe (measured from the center of the hole). The flattened and drilled ends were then bent at an angle of about 17°.
All struts were connected with 2" × ⁵/₁₆" hex bolts. Only 26 bolts and corresponding nuts are required (washers are optional).
To cover the dome, 6 mil plastic sheeting was used (4 mil or thinner is definitely not suitable as covering). The plastic needs to be cut into triangles. There are 2 different triangle sizes: the large (L) triangles have 3 long sides (lll), the small triangles (S) have 2 short and 1 long side (ssl). If the dome is to be covered completely, 30 small and 10 large triangles are required.
On each side of each triangle 9 holes are punched (= 40 × 27 = 1080 holes :-/ ) The plastic triangles are later attached to the pipe structure with cable ties through these holes (each cable tie connects 2 triangles and one pipe). For the complete dome to be covered 585 cable ties are required (9 × 65).

This is the basic shopping list for the Machinism Dome:

The listed material prices are prices for the Southern California area as of Summer 2002, prices may vary in other parts of the USA and even more in other parts of the rest of the world...

Cutting the Cover

First of all, it should probably be said that covering each triangle individually is not exactly the best idea for covering the dome structure. There are probably better and cheaper alternatives. But anyway, the original Machinism Dome was covered with exactly that technique...
With optimal cutting, 2000 square feet of plastic are exactly enough to cover the whole dome with 38 regular (L and S) triangles and 2 special "door" triangles (either L or S) that consist of a separate left and right half. The plastic usually comes in 10 ft × 100 ft sheets and needs to be cut in the following manner:

Each sheet will yield 19 complete triangles and two halves, which can be used as entrance doors.

Spare Parts and Labor

Basically, a structure like the Machinism Dome can be built for about 250 US$. However, this price does not include any labor or any spare parts. There is always a chance that a pipe or plastic sheet is cut wrong and cannot be used. To be on the safe side, it is recommended to have 5 extra EMT pipes, 1 extra roll of plastic, an additional 100-pack of cable ties and some extra nuts and bolts. This adds about another 45$ to the total of the bill.

Labor is another thing that can add to the total cost of the project. Some of the preparation steps require special tools that not everybody might have in the garage... One thing that is very likely to require professional help, is the flattening of the EMT pipes. Contrary to popular belief, this cannot be done with a vise! It requires a tremendous amount of force, which will ruin the thread of the vise after 5 or 6 pipes. The thread will literally get pulverized...
The holes can be drilled with a regular power drill and a good drill bit (or two or three), but this is very tedious. A drill press is actually a more appropriate tool. Cooling is required during drilling.
Also, at least 30 pipes have to be cut to the shorter measurement of the s struts. Again, this can be done with a hand saw and an appropriate blade but is very tedious.
Having the cutting and flattening done by a professional costs between 80$ and 100$ for a bundle of 70 pipes.

Total Cost

The total cost of the Machinism Dome, as it was erected at Burning Man 2002, was roughly 375$, including spare material and third party labor.
There are several ways of cutting down this cost. It is possible to use ¹/₂" pipes instead of ³/₄" pipes, which will reduce the cost by about 75$. However, this version of the dome is clearly not recommended for heavy wind loads (therefore, it would probably not be suitable for Burning Man). After final disassembly at Burning Man, it turned out that even some of the ³/₄" pipes got bent during setup and teardown.
Plastic sheets and cable ties are also very expensive (the plastic as such already costs about 60 to 80$). A cheaper alternative are in fact parachutes, which can be purchased at an army surplus store for as little as 20$. The problem here is that parachutes are designed to catch wind and if they work as designed they can easily carry away the structure in windy weather...

As mentioned already, the idea with the plastic triangles was not the best one anyway. First, it takes a very long time to cover a dome because each triangle needs to be attached in 27 places and the triangles are very awkward to handle (especially during windy weather). Second, the holes tend to rip out very quickly and once one or two holes are ripped, the whole triangle gets blown away very soon...

Acknowledgements

machinism.org wishes to thank Machinism supporter Sandy for the endless hours spent during the initial preparation and test setup phase of the Machinism Dome. Good Job!

Also, a big thank you goes to Frazer Sheet Metal in San Diego for the cutting and flattening of the pipes for the Machinism Dome.