What is a Platonic solid in geometry?
Dec 17, · A platonic solid is a three-dimensional shape whose faces are all the same shape and whose corners are the meeting place of the same number of polygons. Okay, so this sounds like a complicated. Platonic solid, any of the five geometric solids whose faces are all identical, regular polygons meeting at the same three-dimensional angles. Also known as the five regular polyhedra, they consist of the tetrahedron (or pyramid), cube, octahedron, dodecahedron, and icosahedron.
Platonic solidany of the five geometric solids whose faces are all identical, regular polygons meeting at the same three-dimensional angles. Also known as the five regular polyhedra, they consist of the tetrahedron or pyramidcubeoctahedron, dodecahedron, and icosahedron. Pythagoras c. Ghey to Euclid fl. Plato assigned the tetrahedron, with its sharp points and edges, to the element fire; the cube, with its four-square regularity, to earth; and the other solids concocted from triangles the octahedron and the icosahedron to air and water, respectively.
The one remaining regular polyhedra, the dodecahedron, with 12 pentagonal faces, Plato assigned to the heavens with its 12 constellations. Euclid devoted the last book of the Elements to the regular polyhedra, soliids thus serve as so many capstones to his geometry. In platojic, his is the first known proof that exactly five regular polyhedra exist. Almost 2, years later the astronomer Johannes Kepler — resuscitated the idea of using the Platonic solids to explain the geometry of the universe in his first model of the cosmos.
The symmetrywhat is the best wireless card for a laptop integrityand beauty of these solids have inspired architects, artists, and artisans from ancient Egypt to the present.
Platonic solid. Additional Info. More About Contributors Article History. Home Science Mathematics Platonic solid mathematics. Print Cite verified Cite. While every effort has been made to follow citation style rules, there may be some discrepancies. Please refer sloids the appropriate style manual or other likke if you have any questions.
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Read More on This Topic. Learn More in these related Britannica articles:. This principle ro a sophisticated application in…. Early Pythagoreanism acknowledged only four of these, so the discovery of the fifth the dodecahedron, with 12 pentagonal faces was something of an embarrassment.
Perhaps for this reason 5 was often considered exotic and rebellious. History at your fingertips. Sign up here to see what happened On This Dayevery day in your inbox! Email address. By signing up, you agree to our Privacy Notice.
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Platonic Solids A Platonic Solid is a 3D shape where: each face is the same regular polygon the same number of polygons meet at each vertex (corner). A Platonic solid is a regular, convex polyhedron in a three-dimensional space with equivalent faces composed of congruent convex regular polygonal faces. The five solids that meet this criterion are the tetrahedron, cube, octahedron, dodecahedron, and icosahedron. Some sets in geometry are infinite, like the set of all points in a line. Platonic solid. The so-called Platonic Solids are convex regular polyhedra. “Polyhedra” is a Greek word meaning “many faces.” There are five of these, and they are characterized by the fact that each face is a regular polygon, that is, a straight-sided figure with equal sides and equal angles.
The Science of the Platonic Solids There are only five solids that can be called platonic solids — the tetrahedron, the hexahedron or cube, the octahedron, the dodecahedron and the icosahedron. They are also called regular geometric solids or polyhedra and are 3D in shape. Each face of a Platonic Solid is the same regular sized polygon.
The name of each shape is derived from the number of its faces — 4 tetrahedron , 6 hexahedron , 8 octahedron , 12 dodecahedron and 20 icosahedron. For each Platonic Solid, the same numbers of polygons or faces meet at each vertex or corner.
Each Platonic Solid has a dual polyhedron. Platonic Solids, prisms and pyramids , whilst a non-polyhedra solid has a least one of its surfaces that is not flat eg. Platonic Solids Platonic Solids are the building blocks of all existence, including spiritual realties. Why are there only five platonic solids?
The faces of each Platonic Solid are all identical regular polygons. At each vertex or corner at least three faces or more must meet. Note : Two polygons do not build a solid angle. When you add up the internal angles that meet at each vertex, they must equal less than degrees to get a closed solid shape. Note : At degrees, the shape would flatten out to form a plane. Each shape will fit perfectly inside of a sphere, all the points touching the edges of the sphere with no overlaps.
In a nutshell, it is impossible to have more than five 5 , because any other possibility would violate simple rules about the number of edges, corners and faces you can have together and anything else adds up to more than degrees at a vertex or corner. That is, if you join the centres of the Tetrahedrons four faces you get another Tetrahedron. Others believe that the concept of a unified cosmology was well know as far back as at least Atlantas, some13, years ago.
After the world cataclysm occurred that caused the destruction of this and other civilisations, those with knowledge began to come out from the safety of the underground. Wilcock, Some of the oldest examples of the five solids carved from stone over three hundred of them have been unearthed in Scotland. Most sacred and ancient traditions were underpinned by the knowledge of Sacred Geometry, the belief that a hidden order unifies all aspects of the Universe.
With study and visualisation of the underlying geometric forms of this order, the mind can connect to the Oneness of the Universe. This can occur in many ways through the study of mandalas, engaging in dance where the movements and music were in tune with these geometric patterns, and in sculpture, drawing and architecture.
Pythagoras, a Greek philosopher, mathematician and astronomer in the 5 th Century BCE knew of the tetrahedron, the hexahedron and the dodecahedron, learned from Egyptian Sacred Geometry. Collectively, these five shapes became known as the Platonic Solids, after this ancient Greek philosopher.
In this theory, the world was composed entirely of four elements: fire, air, water and earth and each of the elements was made up of tiny fundamental particles.
This was the precursor to the atomic theory. The shapes or particles that he chose for the elements were the Platonic Solids and his intuitive justifications for these associations were:. The tetrahedron was the shape of fire , because fire is sharp and stabbing.
The octahedron was like air , its miniscule components being so smooth that one could barely feel them. Earth consisted of hexahedron , which are solid and sturdy and highly un-spherical. He reasoned that if the elements came in the forms of the Platonic Solids, then each of the solids should stack together, leaving no holes, since for example water is smooth and continuous, with no gaps. He found that the only Platonic Solids that could fill space without gaps were the hexahedron and the tetrahedron, and hence the other solids could not possibly be the foundation for the elements.
Whilst his theory was flawed, because of it the atomic theory was discarded and ignored for centuries. Metaphysically, the Platonic Solids show how all things come from one source and are intimately and permanently woven together. Occurrence of Platonic Solids in Nature. The tetrahedron, hexahedron and octahedron all occur in crystals, but there are a total of 45 other forms of crystals.
Neither the icosahedron nor the dodecahedron occurs in crystals Smith, , pg Flourite, Spinel, Magnetite and Diamond are examples of naturally occurring octahedron formations and pyrite is a hexahedron formation.
Common table salt is an example of how two different elements, sodium and chloride, can bond together and form a Platonic Solid geometry — the hexahedron. The outer protein shell of many viruses form regular polyhedral eg. HIV is enclosed in a regular icosahedron. In biology, Platonic Solids appear in the species called Radiolaria. The Platonic Solids form the building blocks of human bodies, sound, music, language, DNA, planets, solar systems, stars, galaxies and the universes.
A 3D model of any of the elements in the Periodic Table will show a crystalline structure at the atomic level made up of the Platonic Solid shapes.
Because they form the basis of all structure, these solids are used in the study of mathematics, medicine, science, astrology, meteorology and geology, just to name a few.
Sacred Geometry and Platonic Solids. These series of measurements and proportions ordain and organize for us our perception of time and space, as well as our temporary construct of reality. Sacred Geometry for us is a way to represent the Divine through from and shape. The Flower of Life is one symbol of Sacred Geometry and is a visual expression of the connections life weaves through all mankind, believed by some to contain a type of Akashic Record of basic information of all living things.
It consists of six evenly spaced overlapping circles, arranged to form a flower-like pattern. The Fruit of Life symbol is composed of 13 circles taken from the design of the Flower of Life. It is said to be the blueprint of the universe, containing the basis for the design of every atom, molecular structure and life form — everything in existence.
Within this symbol can be found all the building blocks of the universe, the Platonic Solids. Metaphysical Aspects of the Platonic Solids. Platonic Solids often come in boxed crystal sets, and in particular they can be made of the following healing crystals:. Crystal gridding laying out crystals in specific patterns or grids can be aligned to sacred shapes, including the Platonic Solids, to create powerful energy vortices that can be used for healing, atonement, meditation, prayer, distance healing, affirmations, space clearing and energising, communication with Higher Self and connection with the spirit and earth energies.
Platonic Solids are the basic building blocks of all life, the language of creation used and described in many religions and cultures for thousands of years. Each of the Platonic Solids and their associated elements, chakras and energies, are aligned to be used in natural healing, metaphysical studies and spiritual endeavours.
Work with each shape individually or as a collective to tap into their universal power. Who are the Pleiadians Guess where I am as I release this newsletter? I am a Keynote Speaker on a cruise ship to Vanuatu Light Language Light language allows us to pick up information from realms beyond what is commonly accessed Full Name. Email Address.