The Home Dome for many reasons. The short form is a parachute is thin enough to stretch, which catches wind, and rain water. It isn't doesn't breathe very well, but it isn't dustproof. It will also catch on sharp edges of the dome, unless you carefully cover all of them with something like duct tape.
So what properties would we like in a dome cover. It should be waterproof, dustproof, not stretchy, abrasion resistant, light weight, inexpensive, easy to work with, and stay cool in the sun. Unfortunately, no such material exists that has all those properties.
Here is a list of possible dome covering materials, and their pros and cons.
Uncoated fabric: The nylon parachute is an example of this. Lightweight cotton fabric is another possibility. The price ranges from cheap (surplus parachute) to expensive. Can be good for shade. Not so good for high winds, rain, and dust. Easy to snag on sharp points.
Tyvek (made by DuPont): The material of those silky non-woven strong envelope. Made from high density polyethylene fibers. Very reasonably priced from home construction stores. Look for 'Tyvek Home Wrap'. It comes in rolls 9 feet by 150 feet. It costs roughly $50 a roll. It is reasonably waterproof, dustproof, and windproof. It is white, which minimizes heating in the sun. It is reasonably easy to work with. It is pretty strong. If you want a piece bigger than 9 feet wide, you will have to build it from smaller pieces. You can get Tyvek Tape, which is made of Tyvek and has adhesive designed to stick to Tyvek.
Tyvek ThermaWrap (made by DuPont): Same as Tyvek, but metalized. Dupont even has Tyvek Metalized Tape to connect the edges of Tyvek ThermaWrap. I think this is likely the best, coolest, reasonable cost material to cover a dome. If I would have know about this, I would have bought a roll of it. It comes in rolls 9 feet by 100 feet, or 5 feet by 150 feet.
Aluminumized Mylar: Space blanket material. I saw a dome covered with this. No idea where to buy big pieces of it. Probably the ideal material to keep a dome cool. It is very fragile stuff, and rips if you look at it the wrong way. The only practical way I can think of to use this is to have it glued to rigid board insulation, like the Hexaurt construction.
Shelter systems Fabrics: Shelter systems has several woven ripstop films. There is the Translucent Greenhouse Covering, which lets in 90% of light through, their White covering which lets 60% of light through, and Clear Vinyl. The first two are $10 a yard (6 foot wide roll), and the Clear Vinyl is $20 a yard (4 foot wide roll). This stuff is very strong and water and dust proof. Heavier duty than tyvek, and a lot more expensive.
Shadecloth: Made of some synthetic material and designed to make partial shading. Won't stop wind, rain, or dust. Good for doors for privacy, or for ventilation.
Trucker Tarp: Made of 14x14 mesh of 1000 denier nylon threads. 11 mil thick. Grommets at corners and every 3 feet along edge. Reasonably priced. Very heavy duty. Waterproof, dustproof, doesn't stretch, very abrasion resistant. Lets some light through. This is the most abrasion resistant fabric listed. This is also the strongest fabric listed. For high winds, I think it is the best material, due to its superior strength. It also can be bought in large pieces so it is not necessary to put small pieces together to make a bigger piece. The color isn't great to reflect sunlight, but it works reasonably well.
Aluminet: Made by Polysack. Blocks up to 70% of UV. It is an ^1aluminized knit fabric. Not windproof, waterproof, or dustproof. Can be bought in widths up to 28 feet. You can buy it at Gothic Arch Greenhouses. It costs between $0.24 a square foot (for the 30% shade) to $0.31 a square foot (for the 70% shade). Likely will keep a dome reasonably cool, though you will need an inner cover as well to keep the dust, wind, and water out.
Silvicool Tarps: Made by Bushpro Supplies Inc.. A highly reflective tarp. Supposed to last for years. Has loops sewn into the corners and along the edges. Stock sizes up to 18 by 24 feet. Can be made in custom sizes. Looks to be dustproof, waterproof, and windproof. If I was building another cover, I would call these folks up and find out more about this.
Reflectix50: Highly reflective 7 layer thick insulation, 5/16 inches thick. Aluminum color on both sides, bubble wrap in the center. You can buy it at Atlanta Supply Co.. A 50 foot by 4 foot roll costs $61. Likely waterproof, dustproof, and windproof. Not as strong as fabric or tarps.
16 foot dome, in 2000. I wanted a simple, robust cover for it. I decided to use a single rectangular 20 by 30 foot aluminum colored truck tarp. With no seams, there would be no place for it to leak. Obviously, there is no exact way for a rectangle to cover a 1/2 sphere dome without a lot of folding or wrinkling. I did quite a bit of creative folding. I used some grommets at the edges of the tarp as well as some very clever tarp grip clips made by Grip Clips They work very well on one thickness of tarp, and ok on two thicknesses. It wasn't the most elegant solution, but it was simple, robust and weatherproof.
In 2001, I built a 5/8 sphere dome. A single rectangle would fit really poorly. It would also be very large, heavy and bulky. I decided I needed a better solution.
I saw a lot of dome covers, made out of many different kinds of material. Most fit the dome better than my tarps. Some were made out of many individual triangles, each sewn or taped to others. Some were made out of several odd shapes which were multiple triangles, taped or tied together. I decided I needed something better than the 20 by 30 foot tarp I used in 2000. I decided that a 5/8 sphere dome could be approximated as a 9 foot high cylinder with a smaller partial dome on top of it. It is easy to cover a cylinder. I took the old 20 x 30 foot tarp and made 3 rectangular tarps, each about 9 feet high. I purchased a new 30 x 40 foot tarp, and cut off a piece about 9 feet by 30 feet. I folded the edges of my cut tarps, and added grommets to the edges.
I secured the top of the tarps to the top of the second level of triangles. I overlapped each tarp by about 2 or 3 feet with the previous tarp, but didn't secure the edges in any way. For the door, I pulled back one of the tarp intersections. For privacy or dust, just pull the opening closed. If it is hot, the bottom of the tarps can be raised a few feet for ventilation. In a storm, they can be lowered and secured using the grommets and rope.
For the remaining portion of the dome, I used a square tarp, roughly 30 x 30 feet. A hole was cut in the center for the turbine fan. I made my hole too big, so I had to patch it with some extra material. I secured ropes to each corner of the tarp, and dragged it over the top of the dome with some extra help. I went inside the dome, and watched the hole and got it aligned with the turbine fan. Then the 4 ropes were secured to the dome. After that, it is simple to secure the sides of the tarp to the dome. It isn't as pretty as other solutions, but it is very strong, and there are very few seams to fail or leak.