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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 ). 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.
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Platonic solids

Jun 27, 2015

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Page 1: Platonic    solids

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 ).

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.

Page 2: Platonic    solids

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.

Page 3: Platonic    solids

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.

Page 4: Platonic    solids

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 writesthe "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.

Page 5: Platonic    solids

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.

Page 6: Platonic    solids

The Platonic solids and the universe

Thanks to the orbiting Hubble telescope and other new telescopes outside the Earth's atmosphere that have 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 super-clusters of galaxies. Using radio waves, x-rays and other measurements, were located many galaxies 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:

Page 7: Platonic    solids

The mysterious Platonic solids: the figures in the grain

Page 8: Platonic    solids