Flattened icosphere

[Christopher Jones]

A complete radially projected, triangulated icosahedral sphere, considered as a 3D linkage of struts, is rigid, but a truncation removing some of the lower layers is not.

An open geodesic dome is rigid only with adequate base restraint or bracing​.

For a dome which is a projection of the top 15 faces of an icosahedron, for example, the bottom edges are great circle arcs, not flat on the ground. It can, however, be deformed without changing strut lengths to sit flat on the ground.  

The result, as calculated by ChatGPT,  is not very elegant: a model can be viewed here:-

https://3dviewer.net/#model=https://chrisjones.id.au/Spherical%20Tessellations/v16_flat_base_dome.obj$edge_settings=1,000000,0

It is also not viable as a structure, as the struts touching the ground would be under extreme stress.

It nevertheless exists as a theoretical construct...

Chris Jones

[Ashok Mathur]

Can you explain further what you mean by 

An open geodesic dome is rigid only with adequate  base restraint or bracing.

My understanding of tensgrity structures is that they are stable and vibrate around an equilibrium when tension rings are complete .

Theory does not postulate any restraint or bracing?

Regards

Ashok

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[Christopher Jones]

Ashok,

 A geodesic dome made entirely from rigid struts connected by pin joints is not a tensegrity.

Adding a continuous tension ring around the base, however, could store elastic energy and resist changes with a restoring force

with small oscillations possible.   

Regards,

Chris

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[Ashok Mathur]

Dear Chris 

I am happy to learn that the Montreal dome was not a geodesic dome  as per your definition as it was made of rigid struts joined by pin joints.

Regards

Ashok

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