Hi Um-Bot,

Kethisco looks at 1.616, i look at 1.618, it is fun to look at ancient mathematicians, Homer lived around 8th Century BC, Plato was born around approx. 428 BC, Pythagoras was born approx. 570 BC. I don't think that Plato invented Platonic Solids, some would argue that they turned up in Scotland, a 1000 years before Plato, please scroll down to bottom of link to "PLATONIC SOLIDS":-

http://en.wikipedia....ved_Stone_Balls
I think your debate is did ancient mathematicians know something that perhaps is still theory in the present time....perhaps!

The mind set of ancient mathematicians is difficult to interpret, a good investigation of Sacred Geometry, Golden Number, Phi, Fibonacci Series, Fractals, Golden Spiral, CARDIOID, and Chaos Theory is needed!!!!

Plato didn't invent Platonic Solids, but he thought that the Universe was shaped like a Dodecahedron, we can suspect that Pythagoras did as well, picture imaging will join this to Pentacle, Pentagon and Dodecahedron, but it will also join to the Spiral of Life that is seen everywhere plus joined to fractals, so was Plato right?

Perhaps he was right, but we have a long way to go yet in experiments, some scientists think that the Cosmos is shaped like a Dodecahedron, pentacle, pentagon, link below:-

http://physicsworld....-a-dodecahedron
To see how shape evolves by having two opposite pentagons and joining up all points, the Dodecahedron appears in 3D in the centre, link below:-

http://2012forum.com...=4648&mode=view