On the Euler's theorem on polyhedrons.

#######################################################################

"
Only a moron would see beauty in Euler on polyhedrons
What a proud would say so, seeing all or saying so.
"

#######################################################################


Intro:


Chapter 0: A proud 'all seeing' boy point of view
##########

The theorem  "blabla" then s − a + f = 2.
	Where: 	s is the number of summit.
			a is the number of vertices.
			f is the number of faces.

Example for Plato's 5 regular polyhedrons:

 				s 	f 	a
----------------------------
Tetrahedron 	4 	4 	6
Hexahedron 		8 	6 	12
Octahedron 		6 	8 	12
Dodecahedron 	20 	12  30
Icosahedron 	12 	20  30


Comment: nice piece of geometry but this is a corruption for thought.
From the get go, the geometer pretend to be like God "seeing all"  <-- full hubris confirmed.
On a historical note Egyptians were not thinking this way.

Chapter 1: Introducing limits in perception
##########

Directly following Egyptians;
	The only way to instill self limit, doubt and as a result the superiority of God is to formalize our limts with partial blindness.

Starting point: the number 3 for simplicity.

Formalization of the problematic:

		"You are in a room with tree exit points"

			                .
						   / \
						  /   \
						 /     \
						.-------.
					   / \     / \
					  /   \   /   \
					 /     \ /     \
					.-------.-------.

				 Net of the Tetrahedron

		"You perceive only what's on the ground"

With this simple axiom, naturally divides the theorem in two parts:
what you can see with your eyes vs what what is to be seen.

Tetrahedron 	s 	f 	a
--------------------------
Visible         1   3   3
Invisible       3   1   3
--------------------------
Sum  			4 	4 	6   <-- world famous, moronic science.

Conceiting the "You are in a room with tree exit points" pb,
we have to consider tow different ways for exiting the room.

Hard exit: Visible exits, connected to the same level: the ground.
Soft exit: Invisible exit, going up or down.


Hexahedron	 	s 	f 	a
--------------------------
Visible         4   1   4
Invisible       7   5   8
--------------------------
Sum  			8 	6 	12

Going higher in dimension (Octahedron, Dodecahedron, Icosahedron)
is not a good idea. Ezekiel, the one who saw God's awe with his own 'eyes' is much more interesting.