a geodesic sphere model

http://www.instructables.com/id/A-GEODESIC-SPHERE-MODEL/

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A GEODESIC SPHERE MODELby Thinkenstein on June 24, 2009

Table of Contents

A GEODESIC SPHERE MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Intro: A GEODESIC SPHERE MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Step 1: GEOMETRY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Step 2: TOOLS AND MATERIALS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Step 3: CUT STICKS TO LENGTH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Step 4: MAKE A HOLDING JIG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Step 5: ASSEMBLE THE HEXAGON AND PENTAGON UNITS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Step 6: ASSEMBLING THE SPHERE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Step 7: RELATED 3-D MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Related Instructables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8


Author:Thinkenstein author's websiteI'm a refugee from Los Angeles, living in backwoods Puerto Rico for about 35 years now and loving it. I built my own home from discarded nylon fishnet andcement.

Intro: A GEODESIC SPHERE MODELGeodesic dome construction has interested me since the 1960s, when I first became aware of that alternative to square box architecture. Buckminster "Bucky" Fullerpopularized the idea, but as my quick research for this instructable finds, he was not the originator. That credit apparently goes to Dr. Walther Bauersfeld, who used theconcept for the Zeiss Planetarium built some 20 years prior to Fuller's work. This is a Wikipedia link to Buckminster Fuller http://en.wikipedia.org/wiki/Buckminster_Fullerand to Walther Bauersfeld http://en.wikipedia.org/wiki/Walther_Bauersfeld .

Credits out of the way, geodesic domes are beautiful structures. Spheres give the greatest interior volume with the minimum of material. Their basic geometry can bebroken up into hexagons and pentagons, or further broken up into triangles. See the rotating geogedisic spheres on the Buckminster Fuller page.

This model is made up of triangle units, which I then combined into hexagons and pentagons. Those units were then combined to make the sphere. I used bambooshish-kabob skewers from the supermarket (called pincho sticks where I live), and hot melt glue.

Step 1: GEOMETRYAn equilateral triangle is a triangle composed of three sides of equal length. A flat hexagon (six sides) can be constructed out of six equilateral triangles. To more closelyapproximate spherical curvature, you want to raise the center of the hexagon a little. You do this by increasing the length two sides of each triangles, the sides thatradiate out from the center of the hexagon. The longer you stretch the two sides, the more exaggerated will be the peak in the center of the hexagon.

In a flat pentagon (5 sides) the two sides of the triangles that radiate from the center will be shorter than the third side. To more closely approximate a sphere, you have tolengthen them also. As with the hexagon, the amount that those sides are lengthened will determine the height of the peak in the center.

I don't know the math for making triangles that result in a near-perfect sphere, but I find the idea of lumpy domes and peaky geodesic spheres more interesting anyway.Just playing it by feel, this is the design I came up with.

I used the same triangles for making the hexagons and the pentagons. The dimensions I used for the triangles are: 2 inches for the short side, 2 1/4 inches for the longsides. Whatever variations you do with sides that radiate from the center, the outer sides have to be the same so that the hexagons and pentagons will join correctly.(I have plans for making a next-generation model with the hexagon peaks going inward and the pentagon peaks going outward, to make a pollen grain-like structure.)


Step 2: TOOLS AND MATERIALSTools: Cutting pliers to cut the sticksHot melt glue gun

Materials: Flat working surfaceNon-stick work surface cover (Teflon cloth)Vinyl (or cardboard) to make a holding jig for the sticks while gluing themBamboo shis-kebab ("pincho") sticks from the supermarket.Hot melt glue


Step 3: CUT STICKS TO LENGTHRemember that the outside edges of the hexagons and pentagons have to all be the same length. How much you tinker with the inside lengths of the triangle sidesdetermines the amount of peak in the middle of each hexagon and pentagon.

Unless you are really enamored by the way mine turned out using 2 inch and 2 1/4 inch pieces, have fun and create your own variations.

When I decided on the dimensions I was going to use, I cut a sample stick of the two sizes and used those sticks as guides for cutting all the other sticks of the samelength. That way, all I had to do was match up stick ends, butt the cutters up against the other end of the guide stick and snip.

If you use different lengths for the radiating triangle sides of the hexagons and pentagons, you will have to cut three different lengths, not two.

Step 4: MAKE A HOLDING JIGMy work surface is a piece of plywood (a photo collage covers it) with a layer of non-stick Teflon cloth stapled to it. The Teflon is to keep the hot melt glue from sticking tothe plywood. Teflon cloth may be available in kitchen supply centers. (Silicone rubber is another good non-stick material, but you would probably have to make your ownnon-stick sheet by spreading it out on cloth, paper, or some other base material. I use an artist's palette knife to do the spreading.)Over the Teflon cloth, I stapled down some vinyl material as guides to hold the bamboo stick sections. You could probably use cardboard, or maybe ice cream sticks.Leave the corner areas open, since that is where you will be using the glue and you don't want to gum up your holding jig.Once I got the sticks positioned in the jig, I set a weight on them to hold them in place. (I used a big round washer with some magnets stuck to it as the weight.) Thesticks are so light that any pressure from the glue gun can dislodge them if they are not held in place.


Step 5: ASSEMBLE THE HEXAGON AND PENTAGON UNITSI assembled the hexagon and pentagon units by hand, without using a holding jig for positioning the triangles. There is a hole at the center of the hexagons andpentagons. Adjust the triangles to leave a nicely round hole and the rest of the shape will fall into place by itself.Putting in the last triangle of each unit is the trickiest part, since you have to fold the assembled polygons some as you raise the center peak. Fortunately, the hot meltglue is flexible, so joints hinge nicely. The glue also cools and solidifies quickly, so you can hold it by hand until the last glue job hardens up. As you hold it, keep the baseof the hexagon or pentagon unit pressed against the flat base of the work surface so that the base of the hexagon or pentagon will be in a flat plane.

Image Notes1. Hexagon unit completed, with raised peak.

Image Notes1. Hexagon unit flat, before raising the peak.

Image Notes1. Folding the flat hexagon unit to make the peak.

Image Notes1. Flat pentagon unit. The same as the flat hexagon unit, but with one less triangle.


Image Notes1. The holding jig with three sticks ready for gluing.

Image Notes1. Magnets and washer used to weight down the sticks while gluing the triangles.

Image Notes1. Gluing the corners.

Image Notes1. A hole forms at the center of each intersection.

Step 6: ASSEMBLING THE SPHEREEach pentagon is surrounded by five hexagons. Each hexagon is surrounded by three hexagons and three pentagons.

As the sphere grows, it passes through stages that can be used as architectural models for dome structures.


Step 7: RELATED 3-D MODELSThis technique using bamboo sticks and hot melt glue can be used for making other geometry models, which might be of use in classrooms. These are a few othershapes I have made with this technique.


Related Instructables

BambooGeodesic Domeby spotcox

ConstructingGeodesicSpheres onGoogleSketchUp byImperar

Dixie CupSphericalDodecahedronby R.BuckminsterF_cker

Create aGeodesic Domewith BBQ Sticksby Imperar

Geodesic PaperDome (Photos)by watson9194

Multi UseMedia-Pod bygreg0594

Comments10 comments Add Comment

PKM says: Jun 29, 2009. 6:44 AM REPLYHow would you feel about skinning your sphere with paper and putting a lightbulb in the middle? :)

starrymirth says: Jan 21, 2010. 12:53 PM REPLY If you do that, make sure you use an energy saver bulb. I made a similar structure a few years back (en.wikipedia.org/wiki/Small_ditrigonal_icosidodecahedron ) with hot glue and toothpicks -- and covered itwith tissue paper. I hung it up as a lampshade (on an incandescent bulb) and within a few hours it had fallen down to the ground misshapen and somewhat concave... :(

Very nice 'ible!Because you can model almost anything with small enough triangles (as in, for computer graphics) you can make non-regular shapes (like faces, etc.)too. I am however, quite partial to the regular sphere-like shapes.

Thinkenstein says: Jun 29, 2009. 7:28 AM REPLYThis sphere does suggest a lamp to a lot of people. I think getting a light bulb in or out through the triangles would be tricky, though. You would have toleave an opening at the bottom. Skinning all the facets with paper would be tricky, too. It might not be worth all the trouble. It is cool geometry, and it'snice to be able to see through it to appreciate the lines on the back side.

Father Christmas says: Jul 15, 2009. 10:10 AM REPLYNot to mention the fact that, depending on the type of bulb used, you may well melt the glue. Ive had something similar happen. Very disappointing.

ultrajosua says: Oct 8, 2009. 1:23 PM REPLY I just started a big sphere. I used 4inch and 4 1/2 for mine.I'm just a little bit before step 6.I did the first pentagon, 5 hex, and 5 pent. Next layer will be 5 hex. Actually it stands at 12inch high.I used popsicle stick I found in my old appartment. not sure I'll have enough though..


Thinkenstein says: Oct 8, 2009. 6:08 PM REPLYIt looks like a good beginning. I would think that popsicle sticks would be more difficult to work with than the round shishkebab sticks, but aparently theywork well for you. I hope you find enough sticks to finish it.

ultrajosua says: Oct 8, 2009. 6:39 PM REPLY Well, it is kinda hard to get them to fit... since they will never be always edge to edge, they aren't perfectly aligned.

Added a Row tonight using all that was left of stick.Then went to buy all the stick I will need to finish it. Plus all the glue...

Thinkenstein says: Oct 8, 2009. 8:09 PM REPLYIt is looking good.

If you want the corners to be more precise, try marking the end cuts with a pencil and then whacking it with a sharp chisel and a hammer over ablock of wood to make the cut. It should be fairly fast and precise.

You could calculate the angles with math or come close enough with trial and error. When you have your pattern stick you can easily cut copiesof it.

ChrysN says: Jun 28, 2009. 6:29 PM REPLYWow, that looks really cool! Nice work.

Thinkenstein says: Jun 29, 2009. 7:29 AM REPLYThanks.

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