Summary

The 2,3,5 aggregation when viewed along a fivefold axis resembles Penrose tiling of a planar surface. Examples of layers of these aggregations are illustrated in Images 55 - 58.

 

To give an indication of the non recursive nature of these aggregations pentagonal clusters are illustrated in diagram form with the vertices of a regular pentagon defining the centres of the aggregated Phi stella.

To date it has been demonstrated that the original cubic network can transform to an apparently infinite range of configurations including the 2,3,4 and 2,3,5 symmetries of the regular convex solids.

Whether or not the network if activated and left to its own devices would arrive at these configurations is unknown. There is however a natural precedent in that mineral crystals tend toward 2,3,4 symmetry whilst the more recently discovered quasi crystals display 2,3,5 symmetry. Images 73 and 74 are diffraction patterns emitted by mineral crystals. Images 75 and 76 are patterns emitted by quasicrystals.

Given that all the systems illustrated so far are in constant states of transition and can be generated from the original network of cubic cells it is probable they can co-exist at different parts and that, as all parts of the original network are identical, any part has the potential to adopt any configuration as long as there is no loss or gain to the network.

 


logo

Translate