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MATEMATICAS: THE PLATONIC SOLIDS
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De: BARILOCHENSE6999  (Mensaje original) Enviado: 30/03/2014 02:27

The platonic solids

 

 

The platonic solids have certain unique characteristics.

1 All their faces are the same size
2 The edges are the same length
3 The angles between faces are equal
4 All the edges will touch the surface of the sphere

The platonic solids are very important because they are the 5 first basic 3 dimensional bodies that can exist.

 

Their simplicity gives benefits that more complex bodies couldn´t have.

I personally love to build them and enjoy them visually and "feel" their qualities.

 

The tetrahedron has 4 triangular faces. It represents the element Fire. It is the most simple 3d configuration in the universe. It is very strong, that´s why the diamond´s internal structure is tetrahedral.
Fire
 
The hexahedron or cube has 6 square faces. It represents element Earth. . Architects love making houses based in this kind of solid.
Earth
 

The octahedron has 8 triangular faces. Represents the element Air.

It is very strong. My favourite solid.

Air
 

The icosahedron represents element Water

The last "strong" solid.

Water
 
The dodecahedron represents the Vital Energy or Chi. It is the most complex, sacred and unstabe solid of the group.
Vital Energy
 
 

Duals and gender

 
 

The Star Tetrahedron shows how the tetrahedron is dual to itself. The male points up and the female points down.

 

 
 
The cube and the octahedron are duals. Octa is male and cube would be female.In other cases the cube is the male.
Shown left is the deltoidal icositertahedron. Gathering both
The icosahedron and the dodecahedron are a very classy couple.He (icosa) gives her(dodeca) his strengh, and she lends him her divinity.
Shown left is the deitoidal hexecontahedron gathering both at once.

A very uncommon couple. There is a friendship more than duality among the cuboctahedron and the star tetrahedron. I never seen before I built it. The official dual with the cubocta should be the rhombic dodecahedron(shown right).

The official dual with the cubocta is the rhombic dodecahedron (shown left). This solid has the square root of 2 everywhere.
The cuboctahedron is an archimedean solid . It is somewhere in between a cube and an octahedron. Bucky Fuller said the 5 platonic solids are implicit in this body. This solid reproduces the exact geometrical pattern of the original 8 cells of every multi-cellular living creature. This is also shown by the star tetrahedron.
Shown left are the cuboctahedron and the rhombic dodecahedron toether. A complex couple filled with information.

 

Obtaining the Metatron´s cube

1-The fruit of life
Joining all it´s centers
We obtain the Metatron´s cube

 

All 5 platonic solids can be drawn in the Metatron´s cube

Tetrahedron
StarTetrahedron
Cube or hexahedron
Octahedron
Icosahedron
Dodecahedron
   
  Later, Archimedes classified 13 other solids.
1 They all have 2 or more regular polygons.
2 All their edges are the same length.

 



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