A Geodesic Dome

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    A Geodesic Dome

    Some years ago I built a geodesic dome out of inch galvanized steel

    electrical conduit, to serve as an aviary for chickens and small parrots. Iwrote a computer program to calculate the proper lengths of steel tubing,

    and draw the diagram shown below:

    The dome is made from three different lengths of tubing. I used colored

    stickers on the tubes to mark the different lengths -- red for the long ones,violet for the medium lengths, and green for the short ones. You can seethose colors in the drawing.

    The ends of the tubes are smashed flat with a hammer, and then holes are

    drilled in the flat ends for a bolt to go through to connect up to six of thetubes together. Aviary wire is then wrapped around the dome to keep the

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    birds in and predators out. The completed dome is 18 feet high, and over 20

    feet in diameter.

    For this project, something a little more modest in size is required.Something less than three feet in diameter, so it can fit through a door.

    For the first attempt at a smaller dome, I used bamboo kebab skewers andgumdrops. The three lengths of the struts are 100%, 97.85%, and 84.53%.Because I knew I would be using soda straw for the more permanent second

    version, and the straws were 7 inches long, I chose that length for thelong (100%) strut. That made the other lengths 7 inches, and 6 inches.

    You will need these materials for the gumdrop dome:

    90 skewers 7 inches long 85 skewers 7 inches long 80 skewers 6 inches long 11 green gumdrops 15 orange gumdrops 50 red gumdrops Cellophane tape

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    Click on photo for a larger picture

    http://sci-toys.com/scitoys/scitoys/mathematics/dome/first_five.jpg
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    With the sticks all cut to the proper lengths (using a pair of wire cutters) the

    first step is to make the central pentagon of the dome. Five short sticks arestuck into a green gumdrop, and a red gumdrop is stuck onto each of the

    five ends of the sticks.

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    Click on photo for a larger picture

    Next, five medium sticks are stuck into the red gumdrops, and the pentagon

    is no longer flat. We can now see that by making the sticks different lengths,we can ensure that the proper three-dimensional form will take shape.

    http://sci-toys.com/scitoys/scitoys/mathematics/dome/pentagon.jpg
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    Click on photo for a larger picture

    The dome is made of pentagons and hexagons. Each of the five sides of thepentagon has a hexagon attached to it made from the longest sticks. The

    sides of the pentagons and hexagons are all made of the medium sticks. Inthe gumdrop dome we have green gumdrops at the center of the pentagons,

    and orange gumdrops at the center of the hexagons, and red gumdrops

    everywhere else.

    http://sci-toys.com/scitoys/scitoys/mathematics/dome/three_centers.jpg
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    Click on photo for a larger picture

    When five hexagons have been attached to the central pentagon, and fivemore green gumdrops connected at the bottom between the hexagons, we

    have a structure that looks like a dome.

    This is about as far as we can go with gumdrops alone. At this stage, all ofthe weight of the dome is being held up by the stickiness of the bottom

    gumdrops. But gumdrops can only hold a small amount of weight before the

    sticks start to pull out.

    We solve this problem by using cellophane tape to hold the sticks together.

    We only need to do it for the red and orange gumdrops, where we can easilyconnect the sticks in pairs, across the gumdrops. Attach one end of a 4 inch

    length of tape to one stick, lay the tape over the gumdrop onto the oppositestick, and then fold the edges of the tape around the stick so the sticky sideshold together. You can see this by enlarging the photo below.

    http://sci-toys.com/scitoys/scitoys/mathematics/dome/first_dome_2.jpg
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    Click on photo for a larger picture

    We end up with a nice dome. But it won't hold up well to being moved

    around, because the gumdrops are heavy and don't hold the sticks wellenough. But it let us get the concept, and it was nicely color coded.

    Our second, more portable and permanent dome, is made from plastic soda

    straws and small brads, the kind used for fastening paper.You will need these materials for the soda straw dome:

    90 straws 7 inches long 85 straws 7 inches long 80 straws 6 inches long 76 smallbrads

    http://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/half_dome.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpg
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    The first step is to cut all the straws to length.

    Next, poke holes a quarter of an inch from each end of each straw with a

    sharp knife or an ice pick.

    Next, make 6 five-sided stars (from the short straws), and 15 six-sided stars

    (from the longest straws) by sticking the brad through the ends of 5 (or 6)straws, and bending the ends of the brad over to secure them.

    Click on photo for a larger picture

    We begin assembling the dome by connecting one side of the center

    pentagon to one side of a hexagon. The photo shows one hexagon forclarity, but you will be putting two hexagons on at a time, so there are

    always six straws meeting at each brad. The photo also only shows one

    http://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_closeup.jpg
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    medium length straw forming an edge, but you will be adding the edges on

    all sides, closing the brad whenever you have six straws connected.

    Click on photo for a larger picture

    In the photo below, we have five hexagons connected to the centralpentagon, and five more pentagons (without sides yet) connected between

    the hexagons.

    http://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/straw_five_and_six.jpg
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    Click on photo for a larger picture

    The finished dome is 2 feet 2 inches tall (68 centimeters). It is lightweight,

    and can be tossed around without breaking, and will fit through doors, or inthe back of a station wagon. The geometry of the finished sculpture is quitebeautiful.

    http://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/six_fives_and_five_sixes.jpg
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    Click on photo for a larger picture

    The large dome is still housing chickens out in my backyard. It is amazinglystrong -- I had to climb all over it to wrap the aviary wire on it, and it never

    budged.

    http://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/dog_dome_2.jpg
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    Click on photo for a larger picture

    We put a small plastic shed (7 feet high, 6 feet long, 8 feet wide) next to it,and removed three struts to form a door, and screwed the aviary wire to the

    shed, so the shed forms a nice door and "airlock" so the chickens don'tescape.

    A large plastic tarp attached with bungee cords forms a waterproof roof. Thesmall parrots live in the top half of the dome, and the chickens have the

    bottom half.

    A Paper Geodesic Dome

    http://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/dog_and_chicken_dome.jpg
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    Click on photo for a larger picture

    The same ideas can be used to build a dome made from triangular sheets ofmaterial instead of rods. The edges of the triangles simply have the same

    lengths as the rods did.

    If we choose to use paper, we can print out a template on a printer, and

    then simply cut it out, fold it, and tape the edges together to get a dome.

    You can print out the following page from the web site, or make a photocopyof it, enlarging it if you want a larger dome.

    http://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/paper_dome/three_domes.jpg
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    Click on photo for a larger picture

    If you want an even larger paper dome, you can cut the drawing into smallerpieces, so when your printer resizes them to fit the page, you will have

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    larger triangles. Use tape to reconnect the smaller pieces into one large

    piece. In the drawings below, I have duplicated the central pentagon tomake it easy to see how they fit together. You will want to cut one pentagon

    away before taping the pieces together.

    http://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpg
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    http://sci-toys.com/scitoys/scitoys/mathematics/dome/paper_dome/left_dome.gif
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    Click on photo for a larger picture

    http://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpg
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    http://sci-toys.com/scitoys/scitoys/mathematics/dome/paper_dome/right_dome.gif
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    Click on photo for a larger picture

    You can also cut the triangles out of cardboard or plywood, and tape themtogether, so that fiberglass can be applied to make a sturdy building.

    http://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpghttp://sci-toys.com/scitoys/scitoys/mathematics/dome/brad_pack.jpg