Why do we need platonic solids

It has 8 vertices, 12 edges, and 6 faces. Each face is a square. The cube has eleven possible nets. To color a cube so no two adjacent faces are the same color, require at least three colors. It has 20 vertices, 30 edges, and 12 faces. Each face is a regular pentagon. A dodecahedron has possible diagonals.

These are the only three-dimensional shapes that are perfectly symmetrical in every direction, with every internal angle and side length the same. According to Plato, each solid corresponds to a specific element:. The cube corresponds to earth; the icosahedron corresponds to water; the tetrahedron corresponds to fire; the octahedron corresponds to air, and the dodecahedron corresponds to ether. Looking at the shape of the sides, we notice that three of the five Platonic Solids are composed of equilateral triangles — the icosahedron, tetrahedron and octahedron, representing water, fire, and air, respectively.

The two exceptions are the cube and dodecahedron — earth and ether — which are built of squares and pentagons, respectively. The triangle represents the number three, which in the story of creation according to sacred geometry is truly a magic, catalytic number. Three is the number of proliferation and completion. Triumvirates dominate this dimension in the form of Father, Son, and Holy Ghost; Brahma, Vishnu, and Shiva; beginning, middle and end; Mom, Dad, and child; waking, dreaming and deep sleep; past, present, and future; space, time and observer, and so on.

With that in mind, one way to understand the interaction of elements is to see them as sets of triangles crashing into one another and combining to make different sets of triangles. Water, fire, and air are in this constant dance, intermingling to make bigger triangles and dissolving into tinier fragments. Is this not a simplified description of what we call chemistry?

Plato himself is said to have given the following example in order to make abstract teaching more real to our experience.

It is commonly understood that something spicy must be associated with the fire element, and thus the tetrahedron. The tetrahedron is a very sharp shape, with spiked angles that you can imagine would be very prickly if you had several million of them in your mouth. This points to the burning sharpness of spicy food.

On the other hand, more soothing, creamy foods are associated with the water element, and thus the icosahedron. The icosahedron has twenty sides, with much duller angles, very near to a sphere. Compared to the tetrahedron, you can imagine how the roundness of this shape is far more gentle, sweet, and pleasing to the tongue. Air, represented by the octahedron, is nothing but two tetrahedrons stacked back to back.

Ayurvedically speaking, foods with a predominance of the air element is considered very dry and rough, difficult to digest, like popcorn or crackers. There is a certain intuitive logic to how these shapes connect to our experiential reality if you are willing to tune in and do the experiment.

Somewhat outside this process, although not entirely immune, is the square-based cube, representing earth. As the densest element, it makes sense that each of its sides is made of not one, but two triangles aka a square. The eight square sides that make up a cube are indicative of the infinite potential of material creation, as well as the power of stability, as the number eight is both an upright infinity symbol and a perfectly balanced shape suggesting, as above, so below.

Outside the triangular paradigm altogether is the five-sided pentagon that makes up the dodecahedron. Given that the ether acts as a container for the other elements, it only makes sense that it is not overly susceptible to entanglement. That being said, a pentagon can be created by five inwardly-directed triangles though not equilateral , which is appropriate as well, since even the ether is within the third-dimensional realm and not entirely devoid of physical characteristics.

Generally speaking, though, the dodecahedron is the outlier of the group, and rightfully so since its role is to hold space for the ongoing dance performed primarily by the other four elements.

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! There are 5 different kinds of solids that are named by the number of faces that each solid has. These 5 solids are considered to be associated with the five elements of nature i. Earth, air, fire, water, and the universe. Plato, who was studying the platonic solids closely, associated each shape with nature. The 5 times of platonic solids are:.

Plato associated the tetrahedron with fire, the cube with earth, the icosahedron with water, the octahedron with air, and the dodecahedron with the universe.

Platonic solids have their own unique properties that distinguish them from the rest. They are mentioned below:. There are 5 types of platonic solids with unique properties and different shapes.

Let us learn more about the 5 types:. A tetrahedron is known as a triangular pyramid in geometry. The tetrahedron consists of 4 triangular faces, 6 straight edges, and 4 vertex corners. It is a platonic solid which has a three-dimensional shape with all faces as triangles. The properties of a tetrahedron are:. A cube is a 3D solid object with 6 square faces and all the sides of a cube are of the same length. The cube is also known as a regular hexahedron that is a box-shaped solid with 6 identical square faces.

In ancient times some people believed that the whole universe was composed of these special solids. They thought that the earth was made of cubes, the air made of octahedrons, water of icosahedrons, fire of tetrahedrons and that dodecahedrons played a special role in arranging the stars.

You may wonder why there can only be five possible shapes in this special family. There is an easy proof using simple geometry.

First of all we know that at every vertex corner , at least 3 faces must meet. Otherwise the shapes would start to overlap. We can then start looking at regular polygons to see which shapes would work. First of all we will look at equilateral triangles. The next regular shape which is bigger than a pentagon is the hexagon with six sides. There cannot be a platonic solid made up of hexagons — even if three hexagons meet at a vertex this will create an angle of which is too big.