Is there a solution to this mathematical problem

Hi everyone,

I am very skeptical about this, however, in the interest of staying open minded, I feel obliged to challenging my own convictions here and ask the question :

Can one build a dome ( or a part of a dome) from perfectly equal structural members ? I.e. all the struts used in construction must have exactly the same lengths.

Based on my humble understanding of Euclidean geometry, this is not possible, but I would welcome any thoughts on the subject that would otherwise challenge my understanding.

In my research I came a cross geodesic domes, and I now know that even geodesics domes don't have equal members ( well, they have sets of equal members based on the number of subdivisions of the triangular surfaces of an icosahedron )

Thanks.

Replies to This Discussion

Permalink Reply by Daniel Hambleton on April 25, 2012 at 7:49am

Check out zonohedra or minkowski sums...

Permalink Reply by Rémy Maurcot on April 25, 2012 at 9:29am

Hi heider,

Perhaps a picture or diagram rendrais understanding of your message simple.

But i Thinks is possible to divide a dome to equal lenght.

Permalink Reply by Daniel Piker on April 26, 2012 at 6:41am

Hopefully my answer here is useful:

http://www.grasshopper3d.com/xn/detail/2985220:Comment:141774

That just applies to triangles though.

If for example you wanted to make a hexagonal grid on the surface, I found it is actually possible to use equal edge lengths (though a hexagonal grid wouldn't be structurally stable unless the connections are made rigid, and the angles would still vary, so I'm not sure how useful this is).

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