Platonic Solids Sixth Grade Geometry 2. Cube 3. Tetrahedron 4. Octahedron 5. Icosahedron 6. Dodecahedron 7. These shapes are called the Platonic solids, after the ancient Greek philosopher Plato; Plato, who greatly respected Theaetetus' work, speculated that these five solids were the shapes of the fundamental components of the physical universe 9.
Plato associated one solid with each of the four basic elements -- fire, earth, air, and water. He reserved the fifth for the heavens beyond the stars and planets Five Platonic Solids Platonic Solids in Nature Geodesic dome Icosahedron Total views 15, On Slideshare 0.
From embeds 0. Number of embeds Downloads Shares 0. Each face is an equilateral triangle. Of the Platonic solids, the tetrahedron has the smallest volume for its surface and is the only one that has fewer than five faces.
It is one kind of a pyramid. It has 6 vertices, 12 edges, and 8 faces. The octahedron rotates freely when held by its two opposite vertices. It has 12 vertices, 30 edges, and 20 faces. Of the Platonic solids, it has the largest volume for its surface area. Observing the relationships between the Platonic Solids, one may notice that the icosahedron is the precise inverse of the dodecahedron.
This is to say, if you connect the center points of all twelve pentagons that compose the etheric element, you will have created the twelve corners of the watery icosahedron. This is intriguing because what we have thus far been able to observe of the ether indicates that it does indeed behave like a fluid. Granted, measuring and observing the ether has proven rather difficult to this point, due to its all-encompassing pervasiveness. How can one measure something from which one cannot escape?
And if we cannot measure it, how can we be sure that it even exists? We have little trouble measuring the other elements: the kinetic mass of earth; the chemical reactions made soluble by water; the radiant heat of fire; the volts of electric wind. But the super subtle ether evades easy detection. In February of , scientists at LIGO were able to measure actual ripples in the fabric of space-time. This is big news! When the black holes collide, they send waves of gravity rippling out through the very fabric of space-time, just like a still pond disturbed by a stone.
This being the case, we can learn a great deal about the nature of the ether by studying fluid dynamics. Water is far easier to access and observe than ether, so we can take clues from the spiraling of water down a drain, or the path of a hurricane to better understand what is happening at a more subtle level way out in the universe, or way deep within, all the same.
Robert Moon in exploring how the Platonic Solids govern the structure of any given atom, accurately predicting the number of protons found therein. Moon, the eight corners of the cube indicate eight protons. This gives scientific credence to the assertion that the cube shape is associated with the esoteric earth element. Using this model, we can extrapolate the entire periodic table of elements, stacking several solids together to create the larger, less stable structures. This is a very exciting reimagining of how chemistry functions.
This conception of the planetary orbits is not only an elegant wish but a mathematical reality. This is by no means a new idea. Many scientists and philosophers before have suggested that the micro is essentially a reflection of the macrocosm. What is exciting in this case, is the mathematical precision with which we can make this assertion. Such elegant arrangements must be the result of a divine architect.
Whether we choose to name this Nature or God matters very little. What seems to matter is that by studying the creation, we come to better know ourselves as both created and Creator. These shapes, the Platonic Solids, are the letters of the alphabet of the third-dimension. Once we have these as a key, we can decode many of the mysteries of the observable universe.
If these patterns govern atomic structures and planetary orbits, they must also influence the human form, which exists in the exact middle of those micro and macro forces. As an Ayurvedic practitioner, I am extremely excited to continue exploring the potentials for healing offered by this conceptual understanding.
Each of the five elements is specifically associated with one of the five senses, with an organ of action, with color and chakras.
Now we know that they also have a specific shape. What are the practical applications of this knowledge? I invite you to explore these potentials in your own mind and body. Meditate on these shapes and see what changes take place. Practice drawing them, or better yet, build models of the solids using construction paper to become acquainted with their physical qualities.
I promise you such exercises will reveal valuable insights into your own true nature, and literally reshape the way you see the world around you.
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The question is whether you can push and pull all these hexagons around to make each and everyone of them flat. During the imagined bulging process, even one that involves replacing the bulge with multiple hexagons, as Craven points out, there will be formation of internal angles.
These angles formed between lines of the same faces — referred to as dihedral angle discrepancies — means that, according to Schein and Gayed, the shape is no longer a polyhedron. Instead they claimed to have found a way of making those angles zero, which makes all the faces flat, and what is left is a true convex polyhedron see image below. Their rules, they claim, can be applied to develop other classes of convex polyhedra.
These shapes will be with more and more faces, and in that sense there should be an infinite variety of them. For example, dome-shaped buildings are never circular in shape. Instead they are built like half-cut Goldberg polyhedra, consisting of many regular shapes that give more strength to the structure than using round-shaped construction material. However, there may be some immediate applications.
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