SCRIPT PLATONIC SOLID ROCK Source : http://www.youtube.com ...

SCRIPT
PLATONIC SOLID ROCK
Source : http://www.youtube.com/watch?v=Ye24b3ebHcw
Part 1: Prove that there exists only 5 Platonic solids.
00:00
A stranger came upon an ancient ruin and in its stone were carved the following words:
If it is the wisdom of the Platonic solids you seek then through the pentagonal cave you must pass.
The stranger headed to the cave.
The armored ? cave was extraordinary new dimension unlike anything the stranger had ever
experienced.
A disembodied voice began in a rythm enchant, it seemed foreign yet oddly familiar.
Welcome stranger, you have entered the round of the Platonic solid.
I'll show you some worthy of its wisdom.
May it serve you well.
01:09
A fantastic motif dimensional vision emerged.
The first most basic shape is the point.
No dimension says the point, no length, no width, no height.
Two points connected make the second simplest shape, a line.
Just one dimension has the line, length.
Three lines make the simplest two dimensional shape, the equilateral triangle.
Equilateral means all the sides are equal.
The equilateral triangle exists in two dimensions, height and width, no depth.
It takes four equilateral triangles to make the simplest three dimensional shape.
Lay three equilateral triangles together on the plane point to point.
Allow the bodies to rise up out of the plane until their outer edges meet.
Place the fourth equilateral triangle on the top.
The tetrahedron is formed,
tetra means four, hedron means faces.
The tetrahedron has three dimensions, height, width and depth.
02:17
The tetrahedron is the first of the Platonic solids.
A Platonic solid must have the same regular polygons for each of its faces and the same number of
faces meeting together at each corner.
A regular polygon must be a two dimensional shape with all sides of equal length
and all the corners have the same angle.
Some examples of regular polygons are the equilateral triangle, the square, the pentagon, the
hexagon.

02:43
Lay four equilateral triangles together on the plane point to point.
Allow the bodies to rise up out of the plane until their outer edges meet.
Repeat the process, lay one set on top of the other.
The octahedron is formed,
octa means eight, hedron means faces.
03:05
Lay five equilateral triangles together on the plane point to point.
Allow the bodies to rise up out of the plane until their outer edges meet.
Place five more equilateral triangles around the rim.
Repeat the process, lay one set on top of the other.
The icosahedron is formed,
icosa means twenty, hedron means faces.
03:31
Lay six equilateral triangles together on the plane point to point.
Their bodies have no room to rise up out of the plane.
They cannot enter the third dimension.
No more Platonic solid can be formed with equilateral triangles.
03:49
Lay three squares together on the plane point to point.
Allow their bodies to rise up out of the plane until their outer edges meet.
Repeat the process, lay one set on top of the other.
The cube is formed,
the cube is also known as the hexahedron,
hexa means six, hedron means faces.
04:10
Lay four squares together on the plane point to point.
Their bodies have no room to rise up out of the plane.
They cannot enter the third dimension.
No more Platonic solid can be formed with squares.
04:25
Lay three pentagons together on the plane point to point.
Allow their bodies to rise up out of the plane until their outer edges meet.
Place three more pentagons around the rim.
Repeat the process, lay one set on top of the other.
The dodecahedron is formed,
dodeca means twelve hedron means faces.
It is impossible to lay 4 pentagons together on the plane point to point.
No more Platonic solid can be formed with pentagons
05:00
Lay three hexagons together on the plane point to point.
Their bodies have no room to rise up out of the plane.
They cannot enter the third dimension.
No Platonic solid can be formed with hexagons.

It is impossible to lay three heptagons together on the plane point to point.
No Platonic solid can be formed with heptagons.
You have now seen all five Platonic solids,
the tetrahedron, the octahedron, the icosahedron, the cube or hexahedron and the dodecahedron.
No other three dimensional shapes exist having the same number of identical regular polygon faces
meeting at each corner.
Part 2: dual pairs.
05:45
Take a cube, connect the centers of its faces. A small octahedron is formed inside the cube. Let the
octahedron grow, a star shaped structure is formed. This is the stellated polyhedrons. Stellar means
star. Eventually the octahedron completely encloses the cube.
Take an octahedron, connect the centers of its faces. A small cube is formed inside the octahedron.
Let the cube grow, the same stellated polyhedron is formed. Eventually the cube completely
encloses the octahedron.
Because of this relationship between the cube and the octahedron, they're known as a dual pair.
Take a dodecahedron, connect the centers of its faces. A small icosahedron is formed inside the
dodecahedron. Let the icosahedron grow, a stellated polyhedron is formed. Eventually the
icosahedron completely encloses the dodecahedron.
Take an icosahedron, connect the centers of its faces. A small dodecahedron is formed inside the
icosahedron. Let the dodecahedron grow, the same stellated polyhedron is formed. Eventually the
dodecahedron completely encloses the icosahedron.
The dodecahedron and the icosahedron form a dual pair.
Take a tetrahedron, connect the centers of its faces. A second smaller tetrahedron is formed inside
the original tetrahedron. Let the new tetrahedron grow, a stellated polyhedron is formed. Eventually
the second tetrahedron completely encloses the first tetrahedron.
A tetrahedron forms a dual pair with itself.
You have seen that the five Platonic solids can be divided into three dual pairs: the cube and the
octahedron, the dodecahedron and the icosahedron, and a tetrahedron and itself.
At each corner of the cube three faces meet, each having four sides.
At each corner of the octahedron four faces meet, each having three sides.
At each corner of the dodecahedron three faces meet, each having five sides.
At each corner of the icosahedron five faces meet, each having three sides.
At each corner of the tetrahedron three faces meet, each having three sides.
Now that you have gained the wisdom of the Platonic solids you must take leave of this round. May
it serve you well.
The stranger passed back through the pentagonal cave to the world beyond, who was the same
world as before, but in the stranger's eyes would never look the same again.