3.幾何学的変容 Geometrical Transformation


In ancient Egypt, the knowledge of geometry that inherited from Atlantis was sealed. It was the technology lead to a high level of human presence.
In Atlantis period, people found their knowledge without themselves.
They lacked the stage of suitable a certain evolution for the receipt of it. Therefore, the abuse and 
the misuse of the technology that accompanied knowledge were done, and the civilization was ruined.
After the deluge, mankind came to be taken down before the stageand level of civilization to receive it. 
The knowledge of geometry was left only the necessary elements to build a new civilization in their own hand, and made to spread. They were collected and compiled what is "Element ",that became the radical of Euclidean geometry that would build today's material civilization.
There was a limit on this geometry to deal with existence than material.
Therefore, the elements of a Platonic solid has remained nearly two thousand years without progress.The discovery of an innumerable polyhedral group that derived from five polyhedrons was accumulation of the trial rather than wisdom.
However, several factors began to be found as a new breakthrough inthe second half of last century. It is a portal leading to the wisdom of Atlantis.

Keplers Modell of Solar systems ©  from:
Mysterium Cosmographicum (1596)




具体的には、「ゾーン多面体を核にして、その外殻を軸材によって形成することで、規則的な構造を形成する。これが第三の構造体である。Reciprocal frame やMulti-reciprocal Grid などはこのような幾何解析によるものではない。建築への応用として、更にその構造の各構成要素の外方側面を抽出することによってルーフィングを形成する」。


The Platonic solid has become foundation that establishes the Euclidean geometry. The theme of the content described below is the transformation of classical geometry.
Zonohedra are the polyhedra that closely connected with the Platonic solid.
The some typical one had already been found since the Middle Ages.
However, this polyhedron has been studied in earnest since the mid-20th century included.
In the history of the development of geometry, It would play a role to Platonic solids clarify in Non-Euclidean geometry.
I introduce visible forms how the Euclidean geometrical Platonic Solid  will be transformed . 
As the construction this transformation has already been shown in the paragraph of  The third structure.
Concretely, a regular structure is formed with Core Model as zonohedron , and the formation of the outer shell with the axis material. This is the third structure. Neither Reciprocal frame nor Multi-reciprocal Grid are due to such a geometrical analysis. 
As an application to construction, the roof is formed by extracting the structural each component outside side plane in addition.
If this is compared to the walnut, the husk is the structure and the seed that becomes a core model is a Zonohedra And there is a certain law in the orderly forms that appear on the surface.

      ゾーン多面体へ Zonohedron