Choice of Icosahedron by Fuller for geodesic dome

What - with the entire I-beams being woven - or with there being multiple woven layers inside one another? Neither sound terribly promising to me.

Illustrates the general pattern.

The construction is not suitable for "conventional" strut-and-hub domes, though. In that context, the shape isn't even stable.

It works reaonably well as a frame tent, though:

._SCLZZZZZZZ_.jpg Use on a larger scale seems likely to run into material science-related problems.

Of course Fuller was well aware of the pattern - as illustrated by domes such as this one:

No, I was may be too brief. The flanges/web appear as separate structural elements only during initial assembly. But later on, the I-beam gets rigid when its flexible flanges are bolted/fixed using an in-between spacer radial web. Two spheres of slightly different diameter are separately interwoven, placed so that one is enclosed inside the other and is connected at 10 points (or multiple frequencies) by means of radial normal shear load resisting webs. Then we have an extraordinary stiffness of the curved I-beam along all great circles for the entire shell.

Yes, the triaxial weaves imparts shear rigidity eliminating in-plane mechanism like movements. When distance between two inter-connected woven layers is large compared to woven layer thickness, we refer to it as "Isogrid" construction also. Here in-plane stiffness is not orthogonally, but isotropically distributed... to be sufficiently near to a sandwich construction with its inherent flexural rigidity advantage.

Right, but it can be easily built up in the manner suggested, without anyway giving up the overall convenience of fabrication. The flanges can be designed proper length or if too long, can even be coiled up into smaller circles prior to assembly.

In the context mentioned above an integrated flange/web action gives high stability and rigidity from the continuous I-beams .

._SCLZZZZZZZ_.jpg> A thoroughly enjoyable set of small icosi-dodeca tent constructions.

On the contrary, for deeper spherical domes (longitudinal stress compressive and circumferential stress tensile) the triaxial is quite efficient. This can be also checked out on FEA. We know how Fuller pooh-poohed the warnings regarding deep shell tensile circumferential stresses concerns and how his isotropic triaxial beam orientations of the standard geodesic dome triangles efficiently met the loads in tension and compression.

Else, what are the other material science problems?

as this one:

Care to comment about its critical design features and advantages vis-a-vis the multi frequency geodesic dome?.

If we take a figure of merit or structural performance factor such as:

(Static loads on dome + dome weight) * Enclosed Volume / (Plan area * structural weight)

the icosi-dodeca may have a better performance. In any case it appears that this construction would be more efficient than the conventional hub-strut type of geodesic dome construction.

Thanks again for any comments.

Narasimham

My models do illustrate the same geometry as Fuller's dome in Japan - albeit at a lower frequency.

None of the woven domes use "genuine" great circles.

They all tend to deviate from being precise great circles.

This image is quite a good one to see the distortions around the pentagons on:

Such distortions are part of the pattern.

The "octahedron" in the Inagamachi Golf Club Field House dome refers to the shape of the unit cell. Each hexagonal cell was composed of six octahedral blocks - each of which was constructed out of right-angled angle iron.

Each of the black triangles visible on the surface of the dome is the top face of one of these octahedra.

The actual dome itself is of a hex-pent-based geometry - i.e. the vent on top of the dome is a pentagon - rather than a square.

The three-dimensional trusses I can imagine based on the pattern all seem relatively ugly to me.

Failure to form a proper three-dimensional truss would limit the use of the pattern on large scales - IMO.

If you are bending material, that becomes physically challenging when your materials are steel or are wood much thicker than a floorboard.

Material that is weak enough to bend is probably not going to be approved of by the building inspectors as a potentially load-bearing structural roofing material.

Variations on the construction that use straight members - e.g. like the "Nailbanger's Nightmare":

...and my own "Leonardo Fuller" domes:

...still have the problem that forces are applied in the middle of struts. While having some virtues in terms of simplicity, the result is substantially weaker than a hub- and-strut affair made of the same material as a result of this problem.

Generally speaking the pattern is good if you want small and cheap - but I don't think it scales up terribly well.