written by Rene K. Mueller, Copyright (c) 2007, 2014, last updated Tue, January 20, 2015
Due an inspiration by an reader (J. DuPont) of my web-site, who contacted me, I was looking again on the geodesic dome, which I honestly have neglected due the several arguments which arose and I felt more attracted to the bow-based domes like the star dome and the bow dome. But after the hint using a soft pipe as connector, I thought I still have apprx. 130 bamboo sticks left from a yurt building (travel yurt of 4.10m diameter I did in November 2006) and thought, let's try if I can use them for a geodesic dome.
So I used the calculator as listed in the notes I wrote last year and the year before, and the 4V 4/8, which I consider more elegant than the lesser degree of 2V or 3V, almost fit the diameter of my current yurt I live in. For spring I wanted to do a star dome on the same floor and interior of my current yurt (6.4m diameter) but still some tests of the bows is required, so I'm actually consider to do 4V 4/8 geodesic dome of 6.2m or a bit larger of 6.3m diameter beforehand, just the skeleton, and use the same plans for the cover I did for the star dome I planned, so I can exchange the skeleton of the dome setup from "geodesic"- to "star"-dome.
Details I still have to resolve:
- calculating the frame for the skylight, most likely a pentagon - hopefully I can use the same as for the star dome as well
- find a good way to do the door, either triangular, or rectangular to fit the door frame as seamless as possible in the existing skeleton by removing 1-2 struts, details still needed to work out
- 2nd floor with ladder or simple stairs, at 1.7 to 1.9m height and still keeping it portable, did a small sketch for 2nd floor shapes.
4V 4/8 Model
For now I wrote down most of the first decisions. I admit, I'm still vary a bit to go ahead, because since writing on metaphysical aspects of buildings I discovered the ratios and harmonics truly are significant, and in case of the geodesic dome, even with the filigree 4V version, has odd ratios - when looking up in a 4V, e.g. in the model I did, you sense a beauty, but the oddness of the slightly distorted triangles . . . and I guess that's one of the rather significant problems which isn't apparent, the harmonics of the geodesic approach is sacrified due the higher subdivision and approximation to the sphere - whereas the Icosahedron maintains a strict golden mean, the inscribing sphere is
rinner = √(42 + 18 * √(5)) / 12 * s
√(42 + 18 * √(5)) / 12 = 1/Φ = Φ-1
rinner = s / Φ
Φ = s / rinner
the higher subdivisions this gets lost, as there are different strut lengths s.
I'm still researching the harmonics, and still have very few ideas of the meaning of the geodesic dome as such, in a metaphysical sense.
So much, it is based obviously on the Icosahedron, one of the platonic solids - the geodesic dome with its triangle subdivision with approximation of the sphere - bridging the linear regular space of the Icosahedron to the bent and spherical space - a transitional space of linear to spherical space.
Anyway, I still have a dome in mind with uniform length struts, with a clear structure and beauty . . .
maybe the solution is to use 1 or 2 length of struts, and compose a near dome shape - with an even structure, like a series of rings composed of triangles. More background research is required.
While searching for alternatives for the Icosahedron based "Geodesic Dome", I found following resources very inspiring:
Once I explored those in more depth, likely these information will flow into new (to be created) pages on this site.
Update 11. 2. 2007: I just put a comprehensive overview on regular and semi-regular polyhedra, with over 110 convex polyhedra online, essentially platonic (5), archimedean (13) and johnson solids (92).
Update 16. 3. 2007: I finished the comprehensive geodesic approach to various platonic and archimedean solids
4V 4/8 Dome
I couldn't resist to build also the more complex 4V model, 250 struts to cut, from 63 sticks. So, D was 10cm, or 2D 20cm for the calculator:
- r = 32cm, d = 64cm
- A = 8.0cm (x 30)
- B = 9.4cm (x 30)
- C = 9.4cm (x 60)
- D = 10.0cm (x 70)
- E = 10.4cm (x 30)
- F = 9.5cm (x 30)
So, B, C and F are very close, and since cutting so small bamboo so exact is hardly possible for me I made them all the same.
The D and E I marked with color to distinct them.
Following cuts I made then:
- 60x C+D
- 5x D+D
- 30x A+E
- 30x B+F
Step by Step
Starting the 4V Model (also parts for other models)
250 sticks: A, B, C, D, E and F
The PVC junctions, 85x 6-way and 20x 4-way
4V 4/8 Dome Model
Size Comparison with Hand
The 4V 4/8 dome came out very well, the 4mm pipe isn't narrow enough for the bamboo thereby the dome isn't as stable, e.g. when moving around. It would be better to have actually 1mm less diameter of the inner diameter of the pipe than the thickness of the sticks.
So far, the 4V looks more filigree than the 3V I think, less edgy, obvious due higher subdivision.
3V 5/8 Dome, build with bamboo sticks and PVC pipe as junction
In order to explore the Geodesic Dome, I thought to start with a model - using easy available material like bamboo sticks from a garden shop.
has some suggestion about building a model using PVC pipe as junction between dome struts, and this what I did then.
So, I bought
- 150 bamboo sticks (10 packages a 15 sticks), 4mm diameter, 40cm long, and
- 9m PVC pipe outer diameter 6mm, inner diameter 4mm
Cost CHF 18, € 12 or US$15. I used the 3V 5/8 calculator entered Alath+Blath+Clath = 40cm, and dhole = 0.5cm, and got my Alath, Blath and Clath to cut.
- r = 37cm, d = 74cm
- A = 11.9cm (x 60)
- B = 13.9cm (x 90)
- C = 14.2cm (x 120)
so I actually cut for a full sphere, whereas the 3V 5/8 sphere only requires A x 30, B x 55, C x 80. Following cuts I made:
Step by Step
The material: bamboo sticks (40cm x 4mm, 150 pieces), PVC pipe (9m), cord
PVC junction, 1cm for each stick, 0.5cm junction = 3cm length
6-way junction test
My choice to bind it
Preparing the cut of A, B, and C
60x A, 90x B, 120x C
All PVC cut
The knot, step 1
The knot, step 2
The knot, step 3
The knot, step 4
Another approach to bind the PVC pipe, easier than with a cord
A couple of junctions (all 6-way)
3V 3/8 Dome
3V 5/8 Dome
As considered I used the left-over of the 3V and some spare sticks to build a 2V 4/8 Sphere:
- r = 18.3cm, d = 36.6cm
- A = 11.4cm (x 35)
- B = 10.0cm (x 30)
2V 4/8 Dome
2V 4/8 Dome within a 3V 5/8 Dome
It has been quite some fun to build these two models, and also sense the stability within the dome while building it.
(End of Article)
- Page 1: 2014: 5m 2v Icosa, The Numbers, The Details, Connector, Skylight, Door, Cover, Interior, 2006: 6.3m 4v Icosa ...
- Page 2: The Diary, 20. 01. 2015: Little Snow, 18. 01. 2015: A Bit Snow Again, 15. 01. 2015: Struts Replaced & Canvas Put Up Again ...
- Page 3: 20. 2. 2007: Planning Pitch Up, Take Down & Storage, 19. 2. 2007: Completed Struts, 11. 2. 2007: Adding Connectors ...
- Page 4: 18. 1. 2007: Starting with Planning, 10. 9. 2005: Building 4V 4/8 Model, 30. 8. 2005: Building 2V & 3V Model ...