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Recently I helped Luke's classmates make geodesic domes out of newspaper, using this website:
http://www.pbs.org/wgbh/buildingbig/educator/act_geodesic_ho.html
It was very satisfactory: the kids learned about the importance of measuring accurately, keeping track of progress, and how something that looks unimpressive to begin with can be actually amazing at the end.  I was even amazed ("It works!  Math works!" I exclaimed as the kids put the roofs on) and I've done it before.

To give the kids something to look at, we made a sturdier but smaller dome out of straws. I used this website, which has a mix of complete, accurate directions and pictures and vague, inaccurate directions, as well as nice pictures of a chicken run geodesic dome:
http://sci-toys.com/scitoys/scitoys/mathematics/dome/dome.html

One important note: you actually need the following numbers of straws:
  • 90 long (7 3/4") straws, for 6 pointed stars
  • 50 short (6 1/2") straws, for the 5 pointed and partial 5 pointed stars at the bottom, and 
  • 70 medium (7 1/2") straws for connecting the edges of these stars.

The other things that are helpful is to realize that any 5 pointed star could do for the top---so to continue the design, make all the 5 pointed stars have the same configuration around it.  It also helped to look at his paper domes: those were much easier to figure out due to their color.

So here is an attempt at a picture of our dome, rather the worse for wear from being played with by elementary school children.  You can see that it really is sturdy, though: after going through through a couple car rides, being used as a tree topper, being squished through doorways (it actually goes through sideways quite nicely) and the aforementioned children, it still has its characteristic shape.

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