First of all I have to explain you the geometrical theory of this dome structure.
It consists of three type of geometrical category.
First one is as well known platonic bodies.
Those five bodies are able to be circumscribed and inscribed a sphere but also projected on a surface of a sphere.
The basic geodesic domes are made from this principle. and also their structure are used regular icosahedron ,because of the stability by their five pointed stars.
In the second step we need a knowledge about sphere geometry.
In according to its principle subdivision of triangle grids has been possible.
Then in the 3rd step we rearrange those grids on this sphere so that each element construct reciprocal grids. For this analysis we use sphere geometry..
Almost experiment of those structure around the world have been done by only such an analysis.
As a result of this analysis, the bottom element(members)are not able to stand vertical.
Most important point in next step is stability as dome.
In order to solve this problem I put the another geometrical method in this program..
With this theory we are able to set the bottom members vertical to the ground and 15 members are parallel to each other.
you could see those parallel members not only bottom but also around sphere six pieces in all.
It is called "Zone". It is the parallel edge belt of zonohedron. This is main symbolised theory of Zome-geometry or zone
-geometry.
If you interested in this more,I recommend you an official site of W.H.Hart-US.
Zome geometry were known by one traditional geometer H. S. Coxeter-UK during the latter half of the 20th century.
This is most useful theory and method in order to plan reciprocal structural dome so that the dome become stabilized.
In addition to this,this geodesic and reciprocal dome have an ability as transformation .
Then the mathematical formula in excel-program relies upon those theory.
It consists of three type of geometrical category.
First one is as well known platonic bodies.
Those five bodies are able to be circumscribed and inscribed a sphere but also projected on a surface of a sphere.
The basic geodesic domes are made from this principle. and also their structure are used regular icosahedron ,because of the stability by their five pointed stars.
In the second step we need a knowledge about sphere geometry.
In according to its principle subdivision of triangle grids has been possible.
Then in the 3rd step we rearrange those grids on this sphere so that each element construct reciprocal grids. For this analysis we use sphere geometry..
Almost experiment of those structure around the world have been done by only such an analysis.
As a result of this analysis, the bottom element(members)are not able to stand vertical.
Most important point in next step is stability as dome.
In order to solve this problem I put the another geometrical method in this program..
With this theory we are able to set the bottom members vertical to the ground and 15 members are parallel to each other.
you could see those parallel members not only bottom but also around sphere six pieces in all.
It is called "Zone". It is the parallel edge belt of zonohedron. This is main symbolised theory of Zome-geometry or zone
-geometry.
If you interested in this more,I recommend you an official site of W.H.Hart-US.
Zome geometry were known by one traditional geometer H. S. Coxeter-UK during the latter half of the 20th century.
This is most useful theory and method in order to plan reciprocal structural dome so that the dome become stabilized.
In addition to this,this geodesic and reciprocal dome have an ability as transformation .
I will show you one example image.
 |
| transformed structure |
This ability is also the most different feature from traditional geodesic dome.
From the above,in order to meet a condition of the self-sustainable dome with the reciprocal frame we need to take three geometrical step platonic-,sphere-and zome-geometry.
From the above,in order to meet a condition of the self-sustainable dome with the reciprocal frame we need to take three geometrical step platonic-,sphere-and zome-geometry.
Then the mathematical formula in excel-program relies upon those theory.
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