The dome covering is made of several heavy-duty tarps, custom cut and grommetted. We wanted something that would withstand rain, wind, and heat. The tarps are shingled so that rain can't run through into the living space. The side pieces can be rolled up and tied back for airflow on hot days. There's also a hole on the very top for airflow, and it's covered by a raised plastic hat so that rain can't get in. The shingled ends are all lashed down to the bottom struts so that it's under tension, which minimizes flapping in the wind. We get internal tension from plastic snap-on grommets, which are used to anchor the tarps to the vertices.
This picture shows the basic plan, shown in a wormseye view without any shingling overhangs. The biggest piece (A/cyan) covers the top, plus one triangle on the bottom layer. The medium sized B/blue piece covers one whole side of the dome. The other small pieces cover the bottom ring of triangles. Conceptually, it's four parallellogram pieces of three triangles each, plus a door triangle (D/black). But the geometry of the A tarp lets it cover one of those bottom triangles, so one of the bottom pieces (E/green) only covers a two-triangle strip. Two of the parallellograms are (G/white, C/yellow) short-side up, one (F/red) is long-side up.
Here's more pictures, showing a walk around the structure from the sides, and then a birdeye view:
These pictures show the real coverings, overhangs and all.
This is one of the top-short trapezoids (G/white):
Here's side piece C/yellow, the one closest to B/blue, before and
after taking down the top tarp. In both pictures it's partially taken
down itself.
Finally, here's a few shots of the whole thing before covering with tarps,
and after. You can make a simple door triangle, which can either be
tied back out of the way or tied shut when you're asleep or gone.
We used tarp holders to secure the tarp to the vertices, since they
don't create holes in the tarp that would let in rain like metal grommets. They're blue plastic
thingies that you can buy in outdoor stores. We loop a cabletie
through the hole in the tab to lash it to a vertex.
The problem with these tarpholders is that they will pop out when they're under too much load. Grip Clips instead, which I might try next year. The Grip Clips are also easier to position,
This schematic diagram shows the location of the tarpholders. The key
idea is to create tension to minimize tarp flapping, both because the
sound is annoying and because uncontrolled flapping gets worse and
worse as the wind tears the covering apart. On the big top tarp, the
first set of holders goes right below the top pentagon. We also use
holders along the bottom row instead of just lashing with metal
grommets so that we can have the rain-proof overhang. The only
nonobvious thing about the side tarp is the holder in the middle of
the center bottom triangle, which is there to secure a fold necessary
to fit the rectangular tarp to the spherical curvature of the dome.
You need to tie down the overhanging parts of the tarps: keeping them as taut as possible will minimize the flapping in the wind. This is a good idea both because uncontrolled flapping can tear your structure apart, and because flapping is loud and irritating. (You can only minimize, not eliminate, the flapping - in windstorms, the noise can be scarily loud despite your best efforts!) The tiedowns also ensure that the overhang acts as a shingle to keep the rain from running through where the bottom strips of tarps begin.
You should tie down the tarp overhangs at many points, roughly every few feet, using strategically placed grommets. I used 75-pound-test nylon parachute cord, which worked fine. You tie a grommet on top to some spot on the bottom ring of horizontal struts. The best tie-down point is a vertex, since that can give you both horizontal and vertical tension. In some places, when you only need vertical tension, you can just tie it directly to a strut.
You should loop the cord under the strut so that you can get leverage by pulling up tight against it. Tie them as tight as you can, but keep in mind that you'll probably want to go around and tighten them all up every few days or so and during major windstorms, so don't make knots that will be too difficult to take out. I just used triple half-hitches.
Keep in mind that you'll want to keep some triangles completely clear of tie-down cords so that you can easily get in and out. We had an official door triangle, but also used two or three others as main access passages when some of the bottom triangles were tucked out of the way for airflow and visibility.
The long parachute cords are tiedowns for the big overhead tarps, since there's a long distance between them and the bottom ring of struts, and they're intended to always stay tied down. The bottom strip of tarps is different: you want to have the option to move some of them up out of the way for airflow. The tops of those strips are secured to the chest-level struts with cable ties, just like the big overhead tarps. We used two-sided velcro instead of cord for most of the strip bottoms and sides, so that we can quickly fold an entire triangle out of the way. (The bottom strips are also not under nearly as much wind load as the big overhead tarps, since they're smaller, lighter, and more sheltered.) In the picture below, you can't see the velcro strips in this picture shot from the inside, but you can see how a triangle is folded out of the way.
It's important for air circulation to have a hole in the tarp at the top of the dome. We made a little "hat" so that air could flow through but rain would not fall through. The hat is an upside-down plastic tub intended to go under a large plant pot. We drilled three holes in it for little mini-struts for attaching it to three of the five main struts that meet at the top point. Those attachments are made with the same nuts/bolts/washer setup that are at the real vertices.
The hat worked fine in 1999, but in the major rainstorms of 2000 there was a minor leak because the washer setup was not waterproof. Next year we'll try using O-rings at that spot. (The other main strut vertices don't have to be waterproof, since they're covered by tarps. These are the only ones exposed directly to rain.)
I don't have as many details here as for the strut assembly, but here's a few:
The first year we were pretty dogmatic about taking shoes off on the way into the dome, which was a pain to do. The second year we were more lax (except when it was muddy), and just swept the ground tarp clean more often.
A note on disassembly: just fold up the ground tarp and then shake it out back in civilization, where random little bits of food-gunk will biodegrade. Don't shake it out on the playa! (Also, don't forget to shake it out before going back the next year - we forgot about this and had to painstakingly clean it up with brooms when we got back to the playa in 2000, which was a drag.)
Our ladder was just tall enough that one person could fit their arm through the air hole, but not their head. The second person needed to stand on the outside and throw the hat into the hand of the first person like a frisbee, being careful to keep the struts facing up. (You want the smooth plastic side of the hat to be touching the tarp, not the sharp strut ends which could tear it.)
The ladder person needs to catch the hat blind, which is doable with enough tries and yelling. Then the ladder person can turn the hat upside-down and position it so that the bottom of the mini-struts line up with the holes in the three main struts. For each mini-strut, undo the bottom washer and nut, thread the bolt through, re-fasten the bottom washer and nut, and tighten it up.
If we didn't care about rainproofing, by far the easiest thing to do would be to have 40 triangular tarp pieces, one for each triangle. That would be simple to make, since there are only two kinds of triangles: 10 equilaterals with long (cyan) sides, 30 isoceles (with two long, one short sides). This design would work fine for shade, but rain would drip in at all the seams. Shingling doesn't work: just having some overhang between the faces isn't enough, gravity works against us on all the non-horizontal seams.
We vaguely thought about using a parachute since the curvature would be close to what we needed. But we didn't think they were rainproof, we couldn't find one at any nearby surplus store, and some of the ones we saw on the web were really expensive.
Another possibility would be to cover the whole dome with one huge
tarp, say 40'x40'. Problems: that much tarp is really heavy (70 lbs)
and hard to deal with, especially in high winds. It's hard to find
tarps that big, our local stores only had up to 20'x20' or 18'x24',
and they're very expensive. We still would have had to do some amount
of cutting and grommeting to deal with the curvature. It would have
been harder to deal with rolling up the tarp covering the lowest ring
of triangles for airflow, since there would be a lot of overlap
because of the curvature of the dome.
We tried out the blue normal tarps, but found that they just weren't
strong enough. The silver heavy-duty ones are definitely necessary for
this kind of structure. Even with these we had some problems with the
sharp edges of the struts wearing away the tarp at the vertices where
they're under tension last year. This year we're padding with chamois
tape (the kind that you wind on the handles of tennis rackets) to try
to avoid that problem, in addition to reinforcing key points with duct
tape.