I wrote an article recently explaining the basics of geodesic dome frequency, in that article we looked at an icosahedron as the origin of most geodesic domes and some of the basic theories of dome frequency. The conclusion drawn was that the bigger you build a dome the higher the frequency needs to be. When designing domes I find that 2v geometry is OK for domes up to 4 meters diameter (13 feet) after that the triangles get to big and it can be difficult to find stock sheet material to fit very large triangles, so what we do is go up a frequency to 3v, OK we have to fix the flat bottom issue with 3v domes but we can now go up to around 6 meters diameter (19’6”) before the triangles again get to big. So why can’t we just keep going up in frequency?
The problem is as we go up in frequency the geometry gets much more complex:
A 2v dome has 2 different strut lengths
A 3v dome has 3 different strut lengths
A 4v dome has 6 different strut lengths
A 5v dome has 9 different strut lengths

What we need is to maintain the simplicity of a 2 or 3-frequency dome but increase the subdivision of faces so we can build bigger domes without making a ton of different length parts. The answer is to use Pseudo-frequency geometry, sounds complex but in fact it’s really simple. Lets look at one panel of a standard 3v dome, all we do is put three new struts across the center of each panel. See example below:

Take a look at a full 3v dome converted to a pseudo-6v dome.

Advantages of pseudo frequency domes:

Simple geometry, if you can build a 3v dome you can easily add three new struts to each panel and convert it to a pseudo 6v dome.

You could do it after you’ve built a 3v dome to increase strength.

You can build much bigger domes, 11 meter diameter (36 feet) is no problem using pseudo 6v geometry.

Much less likely to get hub inversions on very high frequency domes.

Fitting door openings in a pseudo 6v dome is just as easy as in a standard 3v dome, while fitting door openings in a true 6v dome is a mathematical nightmare!

Disadvantages:

With conduit style domes you will need to flatten a section in the middle of each strut as well as the ends.

If you’re using hubs and struts to build your dome you’ll need to make half hubs that fit in the middle of each strut, and lots of them.

If you have any questions or want advice about building a dome using pseudo phase geometry just leave a comment below:

I would emphasize on the fact that the 3v dome structure should be completed before the additional half struts are added, only to make the triangular sheets half the original size and hence easier to obtain.
If you also want to halve all the strut lengths, I'm am skeptical of the rigidity of a pseudo 6v, since there are flat parts, i.e. the shape is not strictly convex, when convexity is the key factor that makes domes rigid.
Also, I think there's a typo in the image (sudo for pseudo).
Nice ideas in this site!

posted by
Scott

07/09/2011 14:14:02

How complex would it be to build a 50' diameter dome using this technique? Could it be done using 4V instead of 3V?

posted by
jamieclarke

06/10/2011 02:49:13

Hi, Ive already built a 3v 6m diameter dome and now im really really wondering if i can reuse the triangles in a 12m pseudo6v.
My question is, can i keep all the beveled angles at 4 degress for the pents and 7 degrees for the hexs?
Thanks for your great work

posted by
Kadir

15/04/2012 07:24:54

I think you may over estimate the cost of solar and wind. Also cenoidsr he paid less for the house itself ($80k max, as opposed to what $150-$300 depending on where you live). From what I remember solar systems to cover a traditional homes cost about $30k. Domestic one family home wind systems can cost anything between $8-15k (for a fancy one) so all in all I don't see this dome home and the systems would cost more than an average home. I'm sure he's done a lot of itself as well. In fact, didn't he say he built his home this way because he didn't have the money to build a traditional home . I think this former firefighter is Mr Average in terms of economic capability, perhaps even Mr Below Average.

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