I've been interested in building a solar reflector specifically using geodesic geometry.
All I can find at this point is this bare-bones site:
http://www.u.arizona.edu/~shunter/para.txt

The author is a man of few words, and fewer diagrams. I understand the first 2 paragraphs, but deriving the individual triangles is clear as mud. Does anyone have a handle on this method?

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Look at the image of one he made.

If you look at my attached doodle, you can see that each line projected on the parabola has the segments marked either ...,b,a,a,b,... or ...,b',a',b',...
The green dot is the center of the parabola.

If you draw the grid a bit bigger and do the marking you should be able to follow what's going on.

Attached Images

hexparabola.png (6.9 KB, 17 views)

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‘To those who regard “crime fiction” as some sacred icon which must follow a rigid formula, I will always be the man who writes 18-syllable haiku.’Trying to make sense of computers, The Error Log.

There are no "green dots" in his text, but I'm guessing that the "template" labled 1 is the centermost triangle. In 6v geodesic geometry, there is a pattern to how each of the 9 different component triangles fit into the basic icosa-based triangle. In a parabolic version, it's even more complicated since there are 12 more unique triangles due to the directional change of slope.

I guess I could just make a few triangles and treat the problem like a jig-saw puzzle, eventually getting it right.

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OK... I did enlarge your "thumnail" image, and now it's much clearer to me. I should have done that first, but the letters only appeared to be red dots at first glance. Now I see how he managed to get the segment lengths that were not confined along the side of the icosa-based triangle.

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The part that may have confused you is that the parabolic dome is NOT icosa based, there are no points at which 5 triangles are connected.

The Green dot as you probably figured out is only in my drawing.
Template 1 is for the 6 triangles around the center.

Template 2 is the 6 triangles making a star around those and the 12 filling in the gaps between the points of the star.

A point he forgot to mention is that you have to make 6 ab'b triangles and 6 abb' triangles they are mirror images, similar caveats for the rest of his templates.

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‘To those who regard “crime fiction” as some sacred icon which must follow a rigid formula, I will always be the man who writes 18-syllable haiku.’Trying to make sense of computers, The Error Log.

The problem inspired me to make this pdf file, print it, cut it out and glue it together for a simple parabolic hex dome.

It was just one of those perfect problems, 2 hours of figuring stuff out and programming to get the first triangle where it should be, 5 minutes to get the rest.

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‘To those who regard “crime fiction” as some sacred icon which must follow a rigid formula, I will always be the man who writes 18-syllable haiku.’Trying to make sense of computers, The Error Log.

Thanks, good work.
I'll be working on this reflector this weekend. We have a lot of sun that goes to waste here in Tucson. If nothing else, I'd like to make some Solar Chili with the big version I have in mind.
I've also heard of someone suggesting that such a reflector could be used for exploring WiFi hotspots from a long distance. I'll give that a try as well, but now I wonder if there's an optimum size for the reflector in regards to the frequency/wavelength.(?)

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