a MUCH better photo of the icosahedron

[Henry Gould]

Dear Antti,

I am so pleased to learn that you are a Platonist, as many 
mathematicians are.
The six Platonic solids are beautiful. Indeed, there are six not five!
They come in three pairs: Hexahedron (cube) and Octahedron are dual - 
the one has as man faces as the other has edges, both having the same 
number of vertices. The Icosahedron and Dodecahedron are likewise dual 
the same way. Finally the Tetrahedron is dual to itself, to its 
Doppelgänger you see. Thus there are six regular solids, but five 
distinct ones.
The ideas (forms) are eternal and exist whether we mortal, material 
Sequence Searchers sre here or not.
Ah Glaucon, of these things we may speak again someday.

If we demote enough "planets" we could return to Kepler's Cosmographicum 
model of the region we inhabit.

Platonically,

Henry Gould

Antti Karttunen wrote:
> Jonathan Post wrote:
>
>> "Astrological object" an interesting notion, which occurred to me 
>> also.  Given the the Greeks consider the dodecahedron as iconic of 
>> the Cosmos, and the icosahedron is its Platonic solid dual, I think 
>> they were making a categorical statement of morphisms between 
>> cosmologies. The Greeks saw the icosahedron as iconic of the element 
>> "air." Coincidently, "Where does it all end: Search for the shape of 
>> space" is the cover story in the 9-15 December New Scientist.
>
>
> And it is claimed that the truncated icosahedron is responsible for 
> the "Self-organized breakup of Gondwana":
> http://www.mantleplumes.org/EarthTess2.html
> (nice application, at least...)
>
> I will quote from John Baez, from 
> http://math.ucr.edu/home/baez/platonic.html
>
> "Everything sufficiently beautiful is connected to all other beautiful 
> things!
> Follow the beauty and you will learn all the coolest stuff.
> The Platonic solids are a nice place to start."
>
>
>
> Platonically,
>
> Antti
>
>