The document discusses platonic solids, their philosophical significance in ancient Greece, and their connections to art and science. It explains how these solids were perceived as fundamental components of the universe, with historical references to figures like Plato and Kepler, who linked them to the principles of astronomy and physical symmetry. Additionally, recent astronomical observations using advanced telescopes have revealed the existence of super-clusters of galaxies that align with the geometric patterns of platonic solids.

1. In the figures we can see some
examples of poligons: the pyramids of
Cheope ,a ball ,but also some nature
examples like the bacteriophage in
the lower left and the cells of bees.
Platonic solid is the synonymous of regular solid and of convex
polyhedron
and is a convex polyhedron that has congruent regular
polygons for faces ( that is exactly superimposable ).

2. Platonic solids and
phylosophy
 The Platonic solids are five and according to the philosophy they
were the five bases on wich rests the world.
 That is, the smaller forms that organize the visible matter and
invisible. In the “TIMEO” Platon himself describes the tetrahedron
as a “force and germ "of the fire, the octahedron as air, the
icosahedron as water ,the cube as the Earth, and the
dodecahedron represents the image of the universe in its totality.

3. The origins of the solids
 The cube, the pyramid (tetrahedron) and the dodecahedron are
attributed to the Pythagoreans, and the discovery of the octahedron
and the icosahedron goes back to the Theaetetus.
 In particular the discovery of the dodecahedron can be traced to
the fact that in Ancient Greece (especially in Sicily) people found
easy beautiful pyrite crystals of this form.

4. Luck in the history of Platonic solids
The luck of the Platonic solids in thescientific imagination of Western culture has
been enormous.
Art and science blend in a deep, Piero Della Francesca writes
the "de Libellus quinque corporibus regularibus" and Luca Pacioli gives a vulgar
version in the "De divina proportione “. He commissioned 60 plates to Leonardo da
Vinci precisely in order to illustrate the possible variations of simple regular
polyhedra.
Science is no longer seen only as an abstraction or a purely technical but also as a
liberal art. (below you can see on the left "The Flagellation of Christ" by Piero della
Francesca, and right on "De Divina Proportione"). Is interesting to note how in the
work of Piero della Francesca the proportions and harmony are respected.

5. Astronomy, physics and mathematics
with the Platonic solids
 Kepler, known for his enormous contribution to astronomy, tried to
show how the properties of the Platonic solids are closely related
with the regularity of the planetary system.
 In fact, the regularity of the Platonic solids is strictly connected to
the symmetry properties of the physical world.
 The regular polyhedra are also now the starting point of many fields
of research in mathematics and physics.

6. Thanks to the orbiting Hubble telescope and other new
telescopes outside the Earth's atmosphere that have
The Platonic taken more detailed pictures and clear than those from
the ground, it has been possible since 2000, creating
new maps of the sky, galaxies, galaxy clusters and
solids and super-clusters of galaxies. Using radio waves, x-rays
and other measurements, were located many galaxies
the universe are not visible. These data were combined and found
that the super-clusters are collected along known lines
and points of intersection which form at least 4
octahedra premises, which are joined to the vertices in a
kind of crystalline scheme. Among these octahedra and
within them, there are gaps related to magnetic fields
and galaxies should contain a lot of dark matter. This is
the largest structure in the Universe directly observed:

7. The mysterious Platonic solids:
the figures in the grain