Many times reality is something else that we think it is. 

What if we could describe the Universe in the language of mathematics with a graph structure? In the study presented here, I am looking for the answer of this question.

The original motivation of my research was to find a graph in which Albert Einstein’s isotropic light propagating postulate is true. In such a graph, the length of a path is equal between any two points, in case the length path is big enough and the points are at equal geometrical distance from each other. Looking for the solution, I built spatial 3D graphs from frames of polyhedrons. Interestingly, the graphs fit onto one single system: they describe icosahedral structures constructed with identical, edge-fitted dodecahedrons. An edge of the icosahedrons consists of 2-4 solids in the examined cases. These graphs are special, because they contain subgraphs with identical situations. In most cases they form dodecahedral clusters.

In the study, I present these constructions and their graphs in the detail. My research method consists of two alternating elements: constructed models and the verification of their existence with a computer program. The computer drawings presented in the annex of the study, provide the evidence for the graphs’ existence. These 2D drawings were made with the projection of the computed 3D vertex coordinates.

The geometry approach gave interesting results. I found several spatial fivefold rotational symmetrical cases in the built constructions.  The model of icosahedral growth is one of these. The fivefold symmetrical type has been known since the discovery of the quasicrystals. However, at the time of its discovery, it was only projected onto a plane. The structures, I have found and the associated graphs describing them suggest the possibility of a Universe that is constructed from a single element. I had searched the Aether, but I have found a road leading to the cognition of the structures of the particles.


The second layer of the Almassy icosahedron
(overview from it in the 13. chapter)



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