A 3 frequency model dome

With a large 3 frequency dome its important to build a model to follow as things can get complicated. I had made one of these before using straws and sticky-back plastic so got myself loaded up with straws from a supermarket. All the straws I could find had stretchy bits near the top so I cut one to find a maximum strut length I could use. To cut a long story short I came up with a dome radius 35.25 cm for my model.

If you have seen the basic guide to making a model icosahedron you will see it is made up of 20 faces. In a two-frequency dome, each strut length is subdivided by two, creating 4 equilateral triangles on each face.

For the 3 frequency icosahedron each strut length is divided by 3, creating 9 triangles, made up of struts as shown in the diagram below.

2 and 3 frequency faces

2 and 3 frequency faces

In a 3 frequency icosahedron there are 3 chord factors ie three different strut lengths are required. If you get different coloured straws the model works as a useful reference for building full scale. The chord factors for a 3 frequency icosahedron are:

  • A = .3486
  • B = .4035
  • C = .4124

And that formula again: C (chord factor) x R (radius) = length of strut

My sums for the struts were:

  • A= 123mm x 60, colour blue
  • B= 142mm x 90, colour green
  • C= 146mm x 120, colour orange

It took me an hour and a half to cut these and pretty soon I had three piles of straws in front of me, waiting to be connected. I started by connecting the C nodes. I then started connecting the B and C struts, to make a single icosahedron face. Then I went into factory mode and made all of the C connections.

Building the first dome face

Building the first dome face

The dome model takes shape

The dome model takes shape

Bit by bit, the dome took shape and I used a camera tripod to hold the model in a rough dome shape to make all of the connections. Eventually, I had my model three frequency icosahedron.

Completing the 3 frequency icosahedron

Completing the 3 frequency icosahedron

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2 Responses to A 3 frequency model dome

  1. TOM KIRDAS says:

    Did you mean the radius to be 35.25 centimeters, not millimeters?

    Forty-five years ago, I built a 3f alternate icosahedron 5/8 sphere out of electrical conduit pipe — with an 8-foot radius. It took me forever to cut the struts!
    It built it in the yard at my farm (where I still live) – and the neighbor kids came every day to play on it. This was before domes were common fare in public parks and school playgrounds. We eventually hauled the whole thing to my neighbor’s farm because the kids liked it so much.

    Your webpage is an excellent intro to geodesic geometry. I cut my teeth on Domebook2 — way back in 1971. (and still have a copy somewhere)
    THANKS!

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