Space-Plates

[Charles Pegge]

http://www.n55.dk/MANUALS/SPACEPLATESG/spaceplatesg.html (http://www.n55.dk/MANUALS/SPACEPLATESG/spaceplatesg.html)

http://www.n55.dk/MANUALS/SPACEPLATESG/1.jpg

[kryton9]

Thanks I had not seen this technology before, Charles.

I bought a pack of pipe cleaners to try out some ideas for domes yesterday. I live in an apartment so I can only make models for testing ideas now. Once I feel comfortable with a method I will make a bigger one at a park.

Here is the quickest and easiest method I have found so far on the internet that uses pvc piping and plastic ties. http://www.youtube.com/watch?v=VA15YnFDIDw&feature=related

So far I have not seen the wood dowel and rubber tubing and plastic tie dome that I made while living in Ohio. I plan on making a pvc pipe, rubber tubing and plastic tie version.

[kryton9]

I had forgotten how I got around the struts being the same size when I made my dome in Ohio. Playing with the pipe cleaners and triangles of equal size, it triggered my memory after quite a bit of fidgeting to remember that I had looked at the shapes that the triangles ended up making.

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So then I got on the computer and made this using hexagons and pentagons, with all the struts being the same size.
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Here is the result after cutting it out and taping. The benefit of going with fixed polygonal shapes is that it is easier to assemble. You can put the top pieces together first and raise the dome up as you go along. Of course in this paper model it was just folding.
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[kryton9]

Here is a triangle with hexagons. This doesn't give too much protection (coverage). If you join the triangle with the hexagons and their sides, it becomes a vertical structure. Looks better flattened out.
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[kryton9]

11 Pentagons, gives complete coverage.
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[Charles Pegge]

Hi Kent,

As you have seen, regular hexagons and pentagons make the most elegant geodesic domes. Anything more complicated needs a calculator and Spherical Trig!

This HexaPent Frame is about 3.3M across and all the struts are 650mm long, roofing battens (2x1 inch). small metal strips were used to fix the joints. I made this in 2004, before trying more complex designs. It is still my favourite dome geometry.

Charles

PS: Correction to struct length: 650mm


https://lh4.googleusercontent.com/-KH_pvc2-Geo/TzDuxhwpjjI/AAAAAAAAAwo/2QoIEU0Fjeo/s128/dome-fr3.jpg

https://picasaweb.google.com/charlespegge/HexDomeFrame?authkey=Gv1sRgCNfk3pyF5c_e6QE

[Charles Pegge]

There is another shape you might like to try. It is made of 30 identical diamonds (parallelograms). The width of each diamond is in proportion to the fibonacci ratio of its length.

This means each diamond length is 1.6180033.. times its width.

The ends of the diamonds form nodes of 5 embers and the sides form nodes of 3 members.

Charles

[kryton9]

So far that combo looks the nicest in my opinion too Charles. It is lots of fun playing with this stuff. Here is the last of the paper models I made. I did the hexagon pentagon combo, but with a hexagon on top instead of a pentagon.
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One with nothing but hexagons.
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And last nothing but Octagons, but this is going to take too much work, so I stopped at a partial point.
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[kryton9]

I forgot to upload the next step in my tests. I used plastic drinking soda straws with the bendable ends. It sort of turned out lopsided as I built in sitting on the couch, but everyone who has seen has been amazed by how light and strong(for straws) it is. For the next final project I will make it efficient by only having 1 strut for each side, not duplicates as with the straws and over 3 times bigger.

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[kryton9]

Saran Wrap is a good idea John. I gave it to my neighbor's grandkids to play with. They had fun with the paper ones before.

Another good idea for wrapping is the heat shrink plastic wrap they use at markets. I have used the window insulation shrink wrapping before, it costs more than the market wrap so not a cheap option.

I am gonna go back to this store that I saw bamboo rods in the garden section. They had a 25 pack for $4.50 and the rods were 3' long. I hope they didn't sell out.
I will need 55 rods to make that dome with single struts.

[Charles Pegge]

FACES

Hexagons 20
Pentagons 12

EDGES

Quantity 90
Bend angle between hexagon and hexagon 41.8103149
Bend angle between hexagon and pentagon 37.37736814

STRUTS

Quantity as 1 per edge:
between hexagons: 30
between hexagons and pentagons: 60

Length (as proportion of Spherical Radius)

2 * Sin 11.64072314 = 0.403548212

CORNERS

Quantity 60

Each corner connects 2 hexagons and 1 pentagon.
Hexagon Angles: 120
Pentagon Angle: 108

Thus the deficient angle is 12

(For a closed convex 3d surface the deficient angles always total 720)



Charles