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Form, Matter and Memory * Part I

Joao Leao

The Platonic Solids:

As portrayed in Kepler's Mysterium Cosmographicum:

five Platonic solids

with their Empedoclean associations to the universal elements. Though Plato traces the discovery of the regular convex polyhedra commonly associated with his name to Thaetetus, there is good evidence that they have been around since well before greek times. The following stone models were found in neolythic settlements and dated from 10 centuries before the greek miracle.

stone models of the platonic solids

These belong to the Ashmolean Museum of Art and Technology collection (Oxford, U.K.) and reproduced from Keith Crichlow's book Time Stands Still. According to Coxeter other examples of such platonic models were found in etruscan sites predating the golden century by 3 centuries. Incidentally these findings are quite in line with Platonic theory which makes these eternal archetypes intrinsic to the Universal Soul.

Note: Three-dimensional displays of the platonic solids are, of course, available on the Web, either using the sublime new language HotJava (due to Jeff Ewert at Morgan Media) or the no less exciting 3D Web environments VRML or WebOOGL by the nice people of the Geometry Center at the University of Minnesota.



Form, Matter and Memory * Appendices

The Archetopes

The Platonic solids or "archihedra" do represent, to some approximation, the five elements of the greeks in the sense that they can be labelled as mnemonics for the fields that we are able to associate with the modern version of the elemental components of the Universe, namely, fundamental particle fields. This association is discernible through most of the classical spectrum of fundamental theories and some of the early quantum models but its limitations can also be evidenced, specially when one considers the successful instances of the unification os these theories which have come to light late in the twentieth century. The path to the generalization of the Platonic assignment is obviated by the relativistic synthesis and its Minkowskian model of spacetime which suggests that one looks at the mnemonic space Platonic archiedra as 3D projections of 4D architopes which are none other but the 6 regular convex polytopes in four dimensions.



Joao Leao



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page uploaded 26 June 2000, last modified 3 July 2004 Last modified: Tue Jan 4 15:33:54 EST 2000

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