While I might infer the “attributes of Coxeter here,” it is with the understanding such a dimensional perspective which has it’s counterpart in the result of what manifests as matter creations. Yet we have taken our views down to the “powers of ten” to think of what could manifest even before we see the result in nature.
When you go to the site by PBS of where, Nano: Art Meets Science, make sure you click on the lesson plan to the right.
Visitors’ shadows manipulate and reshape projected images of “Buckyballs.” “Buckyball,” or a buckminsterfullerene molecule, is a closed cage-structure molecule with a carbon network. “Buckyball” was named for R. Buckminster “Bucky” Fuller (1895-1983), a scientist, philosopher and inventor, best known for creating the geodesic dome.
Photo Credit: © 2003 Museum Associates/Los Angeles County Museum
Fundamentally the properties of materials can be changed by nanotechnology. We can arrange molecules in a way that they do not normally occur in nature. The material strength, electronic and optical properties of materials can all be altered using nanotechnology.
See Related information on bucky balls here in this site. This should give some understanding of how I see the greater depth of what manifest in nature, as solids in our world, has some “other” possibilities in dimensional attribute, while it is given association to the mathematical prowess of E8.
I do not know of many who will take in all that I have accumulated in regards to how one may look at their planet, can have the depth of perception that is held in to E8.?
One may say what becomes of the world as it manifest into it’s constituent parts, has this energy relation, that it would become all that is in the design of the world around us.
While some scientists puzzle as to the nature of the process of E8, little did they realize that if you move your perception to the way E8 is mapped to 248 dimensions, the image while indeed quite pleasing, you see as a result.
It can include so much information, how would you know that this object of mathematics, is a polytrope of a kind that is given to the picture of science in the geometrical structure of the bucky ball or fullerene.
Allotropy (Gr. allos, other, and tropos, manner) is a behaviour exhibited by certain chemical elements: these elements can exist in two or more different forms, known as allotropes of that element. In each different allotrope, the element’s atoms are bonded together in a different manner.
For example, the element carbon has two common allotropes: diamond, where the carbon atoms are bonded together in a tetrahedral lattice arrangement, and graphite, where the carbon atoms are bonded together in sheets of a hexagonal lattice.
Note that allotropy refers only to different forms of an element within the same phase or state of matter (i.e. different solid, liquid or gas forms) – the changes of state between solid, liquid and gas in themselves are not considered allotropy. For some elements, allotropes can persist in different phases – for example, the two allotropes of oxygen (dioxygen and ozone), can both exist in the solid, liquid and gaseous states. Conversely, some elements do not maintain distinct allotropes in different phases: for example phosphorus has numerous solid allotropes, which all revert to the same P4 form when melted to the liquid state.
The term “allotrope” was coined by the famous chemist Jöns Jakob Berzelius.