In 2006 I started work on a geodesic dome greenhouse. At that time there were fewer resources on the internet for doing this, and I had to derive the formulas for some of the math myself using sites and resources that are no longer available on web. These days I would recommend a calculator like http://acidome.ru to find the exact measurements you need. Nonetheless, all of my numbers are here so that you can see the process.

This dome is a hub-strut wooden structure. To be more precise, it's a 20' frequency 3 dome, 3/5 (or 4/7) sphere using cedar 2x4s. Since eight foot lengths are the most economical, I've adjusted my strut lengths to fit this with two struts per eight foot section. 3 frequency domes have three different strut lengths, each with their own vertex angle. Since I will be connecting these together with hubs for simplicity, I also have to factor the hub size into the strut lengths.

The angles are

A - 10.038 degrees from a right angle
B - 11.641 degrees
C - 11.9 degrees

Internal angles of a regular polygon are given by 180 - 360/n, where n is the number of sides. In this dome, there are 15 sides, so the angle is 180 - 24, or 24 degrees from being flat. Split in two for the contribution from the miter on each strut, gives 12 degrees, which fits nicely with the calculated 11.9 degrees on the C strut which makes up most of the middle circles. The difference comes from the insertion of an occasional B strut and the contribution of the extra-planar tilt.

For practicality with my miter saw, I will simplify these to 10, 11.5, and 12 and expect my hub attachment to give enough to make up the difference.

I will use 3" sch 80 pvc conduit pipe (uv-stable) cut to 3" lengths for the hubs, attached with perforated steel strips. This adds three inches total to the effective lengths of all struts. This is actually a simplification, since the hub widths are not measured at the same angle as the struts will be, but it's close enough. I can't afford to produce materials at greater tolerances, anyway.

3.5" tan 12 degrees = .75", which is the effective overlap obtained when I cut two C struts out of the same 8' 2x4. So, measuring all strut lengths from the outside (longest) edge, I can cut struts up to 8' 3/4" / 2 = 4' 3/8"

Add 3" for the hub, and the effective C strut length will be 4' 3 3/8". I can now work backwards from a reverse strut calculator to find the appropriate lengths for the other two, shorter, strut types. I calculated with decimals for the math:

Laid out as Effective Decimal, Actual Decimal, and Actual Inches:

C - 4.281 - 4.031 - 4' 3/8"
B - 4.189 - 3.939 - 3' 11 1/4"
A - 3.619 - 3.369 - 3' 4 3/8"

So these are the measurements to which I will cut the lumber on the longer edge, mitering at the angles listed above.

There are some fine graphics of the layout of these struts at acidome.ru and similar sites, so I won't attempt to illustrate it here. I will need numbers of struts as follows:

A 30
B 55
C 80

In reality, I'm warping the bottom layer of struts slightly, both to give a more even bottom edge and to normalize the height of the first tier of triangles on the dome. The bottom of a 3 frequency dome isn't quite flat; it bulges and pulls up an inch or so every couple of vertices. In practice we can expect this small bit of warping to cause few problems. Additionally, the edge isn't flat on the ground; it contacts at an angle, since the sphere it projects would be expected to continue at an angle under the ground. Many online calculators can give you adjustments to your struts at the bottom to flatten this out, so I'm not going to walk you through the tedious process of reprojecting the bottom vertices for this.

I need a door in this greenhouse, and after much examination I'm going to put it in one of the hexagons, removing the six internal C struts. I will drop two vertical posts between the top and bottom of the hexagon with joist hangers and use half-sized C struts to brace on either side to the midline vertices. This will connect at a 12 degree angle with the bottom strut of the hexagon. I'll then add horizontal extensions from the side posts to hold a vertical door.

The final bill of cut pieces:

30 A
45 B
10 B flat end
54 C
20 C flat end
2 B half struts
2 vertical door posts

Each individual 2x4x8 will be cut as follows:

2@1 vertical door post each
27@2 C struts each
20@1 B strut, one C flat end each
10@1 B strut, one B flat end each
1@1 B strut, two 1/2 B struts
7@2 B struts each
15@2 A struts each
horizontal door braces will come from scraps from A brace cuts

This adds up to 82 8' 2x4s. Cedar is not the strongest material, but I don't think it will have to be in this structure, and it should hold up to the damp better than fir. At the time of the build it ran $6 at Lowes, for a total of $492, plus tax, not counting any extras I have to purchase for mistakes and the occasional bad section. Today it would be $9 each, for a total of $738. Redwood is much more expensive here. Pressure treated isn't much cheaper, requires more expensive hardware to resist corrosion, and introduces chemicals that I really don't want.

The plan was to glaze with greenhouse film inside and outside (two layers separated by 3.5") the first year and consider things like polycarbonate down the road. I used a radiant barrier on the north wall triangles when I redid the internal plastic the first time.

I should also mention that I deviated from this plan slightly in that I used ground contact pressure treated wood for just the bottom struts. This didn't change the cost.

Step 1: Strut Preparation

72 8'x2"x4" cedar

11 8'x2"x4" structural pressure-treated

Doesn't look like much in the photo, but it felt like a lot when loading and unloading it (and it felt like even more when paying for it!).

Most of the pieces are 3/16" longer than 8'. Cutting at a diagonal of 12 degrees turns 1/16" into sawdust and yields 8' 1/8" on the longer side and 7' 11 3/8" on the shorter side -- a difference of 3/4", as predicted. Apparently I can still do trig after all!

This is good, as I did all my calculations based on overlapping 3/4" on the struts. Also, the extra length in original pieces allows for loss from the sawblade, which I hadn't really thought through.

The picture of cut struts are all out of the pressure-treated lumber: 10 C and 5 B. You can see the chemical penetration on the cut ends. This constitutes everything that will be on the ground. Besides these, the doorway will be made out of pressure treated lumber, consisting of top, sides, and side braces. This stuff must have a stain included because it is orange, rather than the sickly green I associate with ground-contact pressure-treated, especially in the newer high copper formulations.

It's took about an hour to do 30 struts, mostly because I'm being meticulous about the measurements and marking all of the struts on both ends to ensure I can tell them all apart.

Step 2: Hub Preparation

For the hubs I used schedule 80 PVC pipe, 3" diameter, cut to 1/4" less than the width of the struts. Perforated hanger strap, 22 gauge, would be held with two screws on each narrow side of the strut. The screws are stainless steel. The one farthest out is to hold the strap onto the strut and the one closer to the edge is to control pivoting. For the most part, these joints will take compression, rather than tension, so the straps maintain integrity but don't carry much load. Distortion forces should be transmitted through the structure as well, with all parts reinforcing each other. Nonetheless, each strut should be good for up to 320lbs hanging load individually, based on the ratings of the strapping and the pipe. This is important since I want to be able to hang things off of the inside of the frame.

3" sch 80 PVC is very cool stuff--solid, but expensive. Good thing I don't need much (~16'). I no longer have my load calculations, but it exceeded the ratings for the straps, so they won't be a failure point.

Each strap was precut and bent because it's too stiff to bend acutely without a tool and this made it easy to pop into place while constructing the dome.

Step 3: Frame Construction

I initially planned to build the dome from the bottom down, lifting each side to the next row. After seeing how heavy a single hexagon was, though, I scrapped that I idea and went with a bottom-up build.

The first row went very fast, and the second wasn't much worse. It did get a bit confusing remembering where each strut went (the diagrams on sites like acidome.ru are indispensable) but it wasn't bad once I got a feel for how the structure worked.

In the close up of a screw being put in, note that the strap itself is bent out from the wood, so that the point of entry of the screw into the wood is farther away from the center than the hole in the strap itself. This is what pulls the strap tighter when the screw goes in.

Having a second person on hand was important after the second row so that one person could hold the piece(s) in position while the other screwed in the straps. We started preassembling a few pieces at a time and lifting them up together so that we didn't have to do so much work up in the air. The last big piece was two conjoined hexagons that we lifted up and attached all around the edges. After that, all that was left was the center of top pentagon. I attached five struts radiating out from a central hub, and then I carried it up the ladder and poked it through the hole to rest a bit off center on top. It took a bit of work to get all of the spokes butting up against all of the right hubs, but once they were in place everything fit perfectly and I was able to screw them all in without pushing or pulling on anything.

Having the whole frame complete was very satisfying.

Step 4: Dome Covering Pattern

Everyone seems to gloss over this part, but I found it the most difficult to figure out.

I used heavy duty 11 mil woven clear poly from http://www.northerngreenhouse.com for the outer layer of plastic. It has good light transmission characteristics (and strong wind, collision, and UV resistance, which I need), but as a woven material will strongly scatter the light. Even having a second layer of plastic on the inside of the struts will provide some degree of light scattering, though, preventing strong point shadowing from the struts. There will be reflective radiant insulation on the north wall as well, which should brighten things up a bit further by limiting pass-through and providing light from the other side of the structure. The dome shape helps reflect horizontal winter sun down onto the plants from all facets, anyway. The dome is about 13' high, too, and the upper structure captures and bends that light back down.

As far as general constraints on permissivity due to strut coverage, a worst-case back of the envelope calculation would give

Side: 1/4'x4' per strut x ~2/5 dome surface exposure to side radiance

x 60 struts blocking

=60 out of 718 sq ft, or 8% coverage

Top: 1/4'x4' per strut x ~2/3 dome surface exposure to top radiance

x 100 struts blocking=100 out of 1257 sq ft, or 8% coverage

So, 8% is my worst-case blockage due to struts. The actual blockage will be less because this inflates the size of the struts a bit and assumes that none of the radiance on the sides of the struts will make it back into the dome. This will need to be added to shading from the glazing to find final permissivity numbers. Hopefully top dome light gathering and north wall reflection will make up for a bit of this as well.

At this point there is some cutting to do. I've spent a lot of time considering how to cover a sphere with flat plastic without coming to a clear, obvious answer. Covering with a single sheet is not going to happen, because the size of the sheet would necessarily be enormous (better than 80' square) and the waste would be tremendous around the sides. If this were a shelter or something other than a greenhouse I might consider covering with five pieces around the dome (it is 5-way radially symmetric) and refolding wherever needed as I worked my way down the dome. Folding involves greater shading though, and I need to keep the plastic tight for a number of reasons, including standing up to the wind and shedding snow and rain.

I ended up cutting the plastic into the shape of the individual icosahedral patches. If this were a sphere, that would require 20 patches to cover, but it's considerably less for my dome, and should guarantee that everything fits nicely on the structure. The general pattern of these section is in the included picture. The slit is what allows the shape to conform to a sphere and will need to be seamed.

After examining how this would work for the dome, I realized that the top triangle on this patch was not needed. Five of these patches are needed along the bottom (plus five small triangles) and five are needed around the top. However, the top triangle is cut off by the ground line on the bottom patches (these are arranged upside down). At the top, this pattern would result in five corners coming together at the peak, so I opted to remove the top triangles from each piece and lay over a single pentagon piece to minimize problems with leakage.

I'm using the woven plastic material in 10' width, which is just wide enough to accommodate the height of the full triangular patches with sufficient overage to line everything up on the dome and still have overlap. I'm going to use a tarp to trace a template directly on the dome itself, and then lay it under the real plastic to mark each section. I will leave a 6-8 inches of overlap plastic around the pieces to accommodate the seams.The actual attachment to the dome will be done with plastic lathing on the overlapped seam, secured by long staples and wide top nails at strategic points. The trick, of course, will be accessing the top of the dome to put these in.

The plastic is 10' wide X very long, so I unrolled it and restacked it accordion-style to be able to pull it off linearly. After the first couple of pieces I found it easier to use a previous piece as the template for each subsequent piece. The trapezoidal patches are rotated to fit with each other as they come off the roll. Unfortunately, I ran out of plastic, due mostly to my failing to account for the large amounts of overlap that I ended up using on each patch, and I needed to reorder to get a bit more plastic to finish off the external covering. When the second order of plastic came, I had to cut it outside, and that proved more difficult but possible. I would recommend finding a large indoor space if you can, though.

Step 5: Covering the Dome

The sheets of plastic were initially attached with handclamps. Each patch is up to 12' x10', but the center point and interior cut have to be positioned to within 1/2" vertically, horizontally, and rotationally to place the end of the cut right in the middle of the hub and running straight up the strut. I didn't actually cut out the small wedge in the patch diagram; I slit the wedge down the middle so that the two edges would overlap when the piece was wrapped around the (non-flat) hexagon at the center.

When the positioning was right I stapled the plastic lathing onto the center seam by overlapping the cut from above, to allow it to shed water. There is 6-12" of margin around the outer edge of each piece which greatly simplifies positioning but also allows each of the corners to be secured under all of the other seams of the vertex, giving me greater confidence in the integrity of these points.

After I had two of these patches in position I secured the seam between them, reaching the top half from above with a ladder inside the dome, and the bottom half from a ladder outside the dome. On each seam I left the top and bottom edges loose to be able to slide in the adjoining top and bottom plastic.

I continued around until four out of five pieces were in place. I needed to leave one off so that I could get the pentagon at the top attached.

Next, I traced out a pentagon onto my tarp in the same way I had done the previous pieces, including the center cut. Just like the trapezoids, no sliver is cut out of the pentagon--it is just a single cut where the plastic increasingly overlaps outward from the center, in the same way you might make a cone out of a circle with a radial cut in it.

This piece was poked up through the center and positioned around all of the edges and along the cut. Note that on all of these pieces the position of the cut on one of the struts is vital, since the overlap is very small in the middle. Unlike the side pieces, the direction of overlap is unimportant since it does not need to shed water downwards.

Once positioned, I started pinning down the seam of the top pentagon from the open side of the dome where I had left off the fifth side patch. Yes, I'm pretty high in the air here. Note that I'm leaning on the dome itself, and have someone below steadying my 10' ladder.

We decided to cover the center of the pentagon, where the seam comes together in the middle of a hub on a horizontal plane (i.e. it isn't sloped to shed water) with a circular "hat". Thus, a ~14" circle was attached with small strips of lathing on each hub at the top, and the seam lathing came down over the top of that. The pentagon itself is sloped down on each face, so should shed water (though not snow!).

After the hat and seam were attached I went to work around the sides. Each edge was attached from the next triangle over, all around the pentagon. You can see the circular "hat" here as it appears from the inside. The beginning of the seam was started from within the triangle being covered itself, and then the ladder was moved and I came up from within the next triangle so that it could be pulled flat.

I was using extra long staples to be sure that the seams would hold. The electric staple gun allowed me to easily place all of the staples at full arm extension, but because of the long 9/16 staples they didn't fully penetrate the wood unless I really held the gun tightly to the surface. For this reason, I had a hammer up there to pound in anything that wasn't flush. I can't imagine only doing this with the hammer, though, since I generally had to keep two plastic surfaces in tension (opposite directions) under a tensioned plastic lathing strip, and I could not have done this if I needed both hands in order to place a fastener with one and use the hammer with the other. The hand clamps were in constant use and I occasionally tacked a bit of plastic in place with a single staple to keep it there while I held an overlapping piece.

You may be able to see on the picture that the plastic lathing at the ends of each strut is attached on either edge. This is to go around the metal straps that hold the struts to the hubs. Since the edge is thin and weak here, I used more staples. In fact, I used a lot of staples throughout. We've had quite a few wind storms (this area is famous for them) and nothing has loosened in the 65mph gusts. I will also mention here that this woven plastic is quite nice to work with--much sturdier and more resistant to creasing and kinking than any other flexible poly that I've used.

Now it was time to position the fifth side piece. Again, the clamps were used and each side checked. When we were sure of the position, the top and middle seam were clamped and the whole side was rolled up and inserted through the top middle triangle so that I could work on the top seam of the patch. I temporarily tacked the top into place.

The pentagon was folded back down over the side patch, and the lathing on each side of the open pentagon triangle was finished out to the edge over the top of the plastic of the side patch. Then, the last edge of the pentagon was finally attached.

The side patch plastic was unrolled back over the side of the dome, and I moved over to the next triangle to secure the center seam. At this point, the patch was not attached on either side, just at the top. After starting the center seam from inside the triangle, it was finished from a ladder outside the dome. After the seam was finished, each side of the patch was similarly completed from the inside first and then from outside the dome for the bottom half.

With the top half of the dome completely covered, the bottom is sealed with four trapezoids (basically the tessellated patch from the diagram above, minus the top triangle, turned upside down) and five triangle patches (just the top four triangles from the same patch). Then there is the door and the portions around it which will need to be closed up as well. Each lower piece is tucked under the top pieces, whose bottom edges and corners were left open for this purpose.

As in the top patches, the center seams have to be positioned, secured and lathed before the outer seams. At the edges, the bottom patches have to be leaved under the top patches, and the triangles have to be under the trapezoids. There are only five points around the greenhouse where the corners of the patches meet, and for each of these joins there are five corners which have to be layered in the right order. All of the edge seams around one of these vertices are under the lathing before I work on the corner. I tack down the lower layers with a single staple while I pull the upper layers into place so that they can all be pinned under the same lathing. As I mentioned before, this results in the corners all being tacked under the their two opposite seams across the hub, making it even less likely that anything will come loose.

In between the trapezoids are triangle shapes, as I mentioned before, which hardly bear mention since they are trivial to attach from the ground around the dome. The only other oddities were the two pieces on either side of the door which were small and custom shaped to fit. At this point an overlapping flap door or similar arrangement of plastic on the open hexagon would make this a functional closed structure.

Step 6: Door

I'm not a framer, carpenter, or other such, so I'm not going to give advice on how to hang a door. However, I did frame out the hexagon opening to accommodate a full size exterior door.

With this structure I've been trying to stay away from providing a permanent foundation, but this is a problem when it comes to a door which needs to be anchored to the ground in a precise way. Since I planned to add a stone walkway on both sides, I decided to sink some carefully leveled cinder blocks for my doorway support. I know from past experience that this kind of arrangement is very stable in my soil and climate, and unlikely to shift. It would not have worked at all on my previous property where everything was always sinking and drifting, but the blocks I set at a property nearby were still level and in position after 25 years, so it seemed safe.

The uprights were reinforced and braced. This was much harder than I expected because my wood was not straight. If there was one thing I could change about the door, it would be ensuring that both sides were as true as I could get them, and then doubling them up to make sure they stayed that way. As it was, shimming and adjusting was very difficult, and I used special screws so that I could adjust the push & pull between the door frame and the supports, rather than just holding it tight to it. I'm a much better gardener than I am a carpenter or framer

.I used a section of the thick outer plastic as a barrier between the door threshold and the bricks. This was further covered by mats on the inside and out, and sealed around with rocks. The door itself has a low-E (doesn't pass infrared) double pane glass inset and extra weatherstripping for a good seal.

Step 7: Ceiling Fan

Running electricity was probably the same as for any greenhouse. I dug a trench 24" deep (deepest frost line in the area is 18" here) and dropped a conduit in with four strands of 6 gauge outdoor rated wire. I won't go into wiring details, since you really need to check your local codes and get a certified electrician to help with this part. There is an outdoor spa-type box/GFCI/emergency shutoff on a post in the greenhouse to which everything connects.

The large gap where the trench turns had a three foot rock in it that had to be removed.

I purchased a wet location ceiling fan, since I had extra vertical space and the shape of the structure seemed ideally suited to it.The first step to mounting it was placing the fan-rated wet seal junction box at the very apex of the structure. I carefully positioned the tabs over the struts and screwed it down with stainless steel screws. Then I attached the hanging frame that came with the ceiling fan.

Electricity was provided by a half inch conduit attached to the ascending struts. I had to pre-bend the conduit for a while so that it wouldn't pull too hard against the brackets when I attached it to the curving structure. It is glued in to junction boxes at the top and bottom to seal it.

I purchased an 18" extension rod for the fan to drop it down from the curving sides. Wiring it all up was pretty much the same as handling any ceiling fan, according to the directions. It hangs from the bracket while all of the wires are connected up and the covers put in place. Then, each of the blades are added and balanced, again according to the instructions that come with it.

The fan has been constantly running essentially since I put it up a couple years ago. In the summer I direct it downward and in the winter I direct it up. Either way, the leaves in the greenhouse show a constant rustling and I'm satisfied that the circulation is adequate. Thermometers placed at various heights and distances from the center have shown an even temperature in both hot and cold weather. Perhaps the greatest advantage to this arrangement has been that I can place strong fans next to the door and keep the internal temperature within 5 degrees F of the outside even in the heat of summer without the top vent that I always assumed would be necessary.

After eight years, I was moving a ladder in the greenhouse and accidentally stuck it into the spinning blades. The weathered blades shattered. $20 got me a set of generic blades of the same size, and the fan was back in operation.

Step 8: Interior Plastic Layer

Before the fan was hung, but after the bracket and conduit were in place, I added the internal layer of plastic to the structure. For this, I started with a 20' square piece of 4 mil poly film. Because of the way that it was folded, it was easy to located the center and place it over the fan mounting. A short length of plastic lathing was attached over each of the five central struts to anchor the plastic. This had to be done while carefully supporting the connections from inside the cascading plastic to prevent the weight of the piece from pulling itself down before it was fully anchored. Once these attachments were made I no longer had to worry about it crashing down around me while I worked on it.

I worked my way down from center, one tier at a time, tacking a small piece of lathing below each hub and pleating where necessary to take up any slack that appeared as it curved down. As long as I didn't try to move down before every attachment at a given level was complete I didn't have too much trouble molding my plastic to the concave surface. I was impressed by how little I needed to overlap this way.

Once I ran out of plastic at the bottom edges, I started at the door and added 10' tall x 20' wide pieces of plastic around the sides until I had worked my way completely around. These were a bit trickier, and I ended up with a few pockets where I couldn't push the plastic out to all of the hubs.

When I replaced the the interior plastic I first put up reflective radiant barrier on the north side. Then, after putting up the top plastic piece, I attached the bottom pieces near the bottom set of hubs (at ~3' high) first and then pleated upwards, which worked better. I don't have pictures of this second covering effort, though.

Step 9: Final Thoughts

With a single 1500 watt, 120 volt heater I can maintain a 20 degree F differential to outside temperatures throughout the winter. It takes 14000 BTUs to reliably provide the 40 degree differential required by our coldest days most years, including losses due to safety venting. If I were to better insulate the bottom portions of the structure and the north wall, as originally planned, and switch all of my heating to electricity, as still planned (hydroelectric is cheaper than gas here, even for heating) I could certainly realize greater economies of heating.

The original plan was to run as much as a 65 degree differential, with 30000 BTUs of available heating, and I may work toward that when I replace the cover again this next year. I do maintain ponds, aquariums, and fresh water storage totaling about 1000 gallons in the greenhouse, which provides some thermal ballast. I have no idea how much, since they have been present since before I sealed the structure.

For a while I had installed low pressure misters on the second tier ring (~7' up) around half the greenhouse. These provided 15-20 degrees of cooling when run 5 minutes at 20 minute intervals during our 115 degree weather, keeping things below 100F. Unfortunately, they clogged easily and were difficult to fix without replacing all of the emitters, even when I placed multiple filters on the inline. A high pressure system would probably work better, with a booster pump

I've mostly kept a bare floor, with various types of rock or rubber mats in places. I know this is unusual, but it works for me. If you want a fancier floor, it should be similar to installing such in any greenhouse.

Costs:

Basic Frame - $700
Glazing in and out - $300
Other parts added - $600

I would add 50% to these costs today, mostly to account for greatly increased transportation expenses (which gets bundled into the price of goods as well as direct shipping), but also inflation.

Frame costs are mostly dependent on the price of lumber.

Quality glazing always represents a significant cost, and I think the amount listed is lower than usual. Unfortunately, poly film is only rated for four years and has to be repurchased and installed. Although I've replaced the internal plastic twice in 12 years, I highly recommend the woven external material for its strength, ease of handling, durability, and scattering light transmission. I'll be replacing it this year for the first time.

Other parts' cost will be higher or lower depending on choice of door, vents, heating and cooling system, etc. This number probably has little relation to the type of greenhouse constructed, and is probably least informative for someone trying to construct a similar structure.