Geometry rules the order of Nature.
Euclid grouped the 5 solids and on an interpretation of geometry that bears his name (Euclidean), the basic concepts of the puzzle.
These were consolidated with the acceptance that crystals of metals of the periodic table of Mendeleyev (Russia 1834-1907) belonged to the same pattern of a crystal diffraction where the distribution of bright dots describe the arrangement in accordance with a hexagonal pattern.
The pattern of a quasicrystal of Al, Cu, Fe, was discovered only in the late nineteenth century, until then denied.
This belated merit was assigned to the recent Nobel Prize in Chemistry: Daniel Shechtman for his discovery of quasi crystals in 1982, when he found an alloy of Al and Mn, which apparently had a symmetry of order 5, forbidden until then in mathematics.
Remember Euclides? Can you imagine how much science as “modernism” has passed under the bridges?
For example . Shechtman “discovered” quasi crystals.
The traditional method for the growth of them, is based on the rapid cooling of molten metal so that the atoms do not have time to access the equilibrium positions corresponding to the common crystalline solids.
Returning to the geometrical morphologies of quasi crystals vs. periodic crystals. We met diffraction patterns of crystals (Euclidean) vs. quasi crystals (Shectonians).
The first match hexagonal morphology geometric pattern.
The second, for centuries ignored, respond to a pattern of diffraction of pentagonal-geometric (quasi crystals of Al Cu Fe)
The pattern of electronic diffraction quasi crystal Al Cu Fe, is the largest example of perfection in Φ and Φ Bonacci morphologically that Man has discovered on the planet until now …….