Platonic solids
Platonic Solids are the building blocks of all existence,
including spiritual realties. … They encapsulate our understanding of the universe.
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.
Crystal Platonic Solids
Definitions:
♦ A polyhedra solid must have all flat faces (eg. Platonic Solids, prisms and pyramids), whilst a non-polyhedra solid has a least one of its surfaces that is not flat (eg. cylinder, sphere or cone).
♦ Regular means all angles are of equal measure, all faces are congruent shapes or equal in every aspect, and all edges are of equal length.
♦ 3D means that shape has width, depth and height.
♦ A polygon is a closed shape in a plane figure with at least five straight edges.
♦ A dual is a Platonic Solid that fits inside another Platonic Solid and connects to the mid-point of each face.
Why are there only five platonic solids?
There are a number of rules that apply to 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 360 degrees to get a closed solid shape.
Note: At 360 degrees, the shape would flatten out to form a plane.
A regular triangle has internal angles of 60°, so we can have:
♦ 3 triangles (3×60°=180°) tetrahedron
♦ 4 triangles (4×60°=240°) octahedron or
♦ 5 triangles (5×60°=300°) icosahedron
all of which are less than 360 degrees
A square has internal angles of 90°, so there is only:
♦ 3 squares (3×90°=270°) hexahedron
A regular pentagon has internal angles of 108°, so there is only:
♦ 3 pentagons (3×108°=324°) dodecahedron
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 360 degrees at a vertex or corner.
Other Interesting Symmetry Facts about Platonic Solids
Symmetry of Platonic Solids
Hexahedron & Octahedron
- They both have the same number of edges, being 12
- The number of faces and vertices are interchanged
♦ Hexahedron has 6 faces and 8 vertices
♦ Octahedron has 8 faces and 6 vertices
Dodecahedron & Icosahedron
- They both have the same number of edges, being 30
- The number of faces and vertices are interchanged
♦ Dodecahedron has 12 faces and 20 vertices
♦ Icosahedron has 20 faces and 12 vertices
Symmetry of Mapping One Solid Into Its Reciprocal or Dual
♦ If you connect the centre of all the faces of the Hexahedron you get the Octahedron
♦ If you connect the centre of all the faces of the Octahedron you get the Hexahedron
♦ If you connect the centre of all the faces of the Icosahedron you get the Dodecahedron
♦ If you connect the centre of all the faces of the Dodecahedron you get the Icosahedron
♦ The Tetrahedron is self reciprocating. That is, if you join the centres of the Tetrahedrons four faces you get another Tetrahedron.
History of Platonic Solids
Many believe that the five regular polyhedra were discovered by the ancient Greeks who called them the “atoms of the universe”. Others believe that the concept of a unified cosmology was well know as far back as at least Atlantas, some13,000 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. Eventually, as those with scientific knowledge emerged, the ‘big picture’ of the truth of these solids was lost. (Wilcock, 2002).
Some of the oldest examples of the five solids carved from stone (over three hundred of them) have been unearthed in Scotland. They date back to Neolithic times, around 2000 BCE (Before Common Era), but their purpose is still a mystery today.
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 5th Century BCE knew of the tetrahedron, the hexahedron and the dodecahedron, learned from Egyptian Sacred Geometry. Plato (427-347 BCE) in his ‘Theaetetus’ dialogue, a discussion around the question “What is knowledge?” that dates to about 369 BCE, added the octahedron and the icosahedron. Collectively, these five shapes became known as the Platonic Solids, after this ancient Greek philosopher. Struck by their beauty and rarity, he speculated that these five solids were the shapes of the fundamental components of the physical universe, what he called the “Theory of Everything”.
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.
- Water was made up of icosahedra, which are the most smooth and round of the Platonic Solids that flows out of one’s hands when picked up as if made of tiny balls.
- Earth consisted of hexahedron, which are solid and sturdy and highly un-spherical.
- The dodecahedron, left unmatched to one of the four elements, had twelve faces that Plato decided corresponded with the twelve constellations of the Zodiac and was the symbol of the ether or universe or spirit, writing, "God used this solid for the whole universe, embroidering figures on it”.
Aristotle (384 BC – 322 BC) was one of Plato's students. 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.
What Platonic Solids Mean for Current and Future Generations
Plato's theory, in which the elements are able to decompose into "subatomic" particle and reassemble in the form of other elements, can be considered a precursor to the modern atomic theory. Aristotle's question about the kinds of shapes that fill space, has proven to be crucial to the study of crystals where atoms are locked into repeating geometric patterns in 3-dimensional space. 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, 1982, pg 12). 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
Sacred Geometry is visible everywhere you look in nature: from the spirals of the nautilus shell, the sunflower and galaxies, to the hexagons of snowflakes, flowers and a bee’s honeycomb. It is also known as Language of Light and can be defined as “the study of the connections between proportions and forms contained in both the Microcosmic and Macrocosmic Dimensions with the purpose to understand the Unity and Oneness that underlines all Creation and life. 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. Through its conception of forms, it embodies the perfect marriage between the Earth and the Heavens, or physical reality with the energy of the Sacred”.
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. From the Flower of Life comes the Seed of Life, the Egg of Life, the Fruit of Life and the Tree of Life. The Flower of Life can be found in the temples, art and manuscripts of cultures, including: Egypt (Mount Sinai), Hungary, Israel, China (Forbidden City), Japan, India, Bulgaria, Turkey (Roman sites), Spain, Austria, Italy, North Africa (Morocco), Middle East (Lebanon, Islamic mosques), South America (Peru), North America (Mexico) and Great Britain (Westminster Abbey).
The Flower of Life symbol can be used as a metaphor to illustrate the connectedness of all life and spirit within the universe, an instrument of dialogue between man and God, permitting us to find unity inside nature’s diversity.
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. If each circle's centre of the Fruit of Life is considered a "node", and each node is connected to each other node with a single line, a total of seventy-eight lines are created, forming Metatron's Cube. Within Metatron’s Cube, the Platonic Solids are formed, as well as the Merkaba (Star Tetrahedron, the spirit or energy body surrounded by counter-rotating fields of light, or spirals of energy such as a strand of DNA, which transport spirit or consciousness from one dimension to another).
Metaphysical Aspects of the Platonic Solids
Hexahedron
♦ Earth Element
♦ Root Chakra
♦ Sits flat and firm, is solid and sturdy
♦ Key Function: grounding
♦ Reconnects energy to earth and nature
♦ Regaining refocus
♦ Removing tension and easing physical stresses
♦ Great for work, in car, children and pets.
Icosahedron
♦ Water Element
♦ Sacral Chakra
♦ Key Function: transformation
♦ Helps one go with the movement, flow and changes of life effortlessly
♦ Teaches us to ‘go with the flow’
♦ Enhances the creative thought process and freedom of emotional expression
♦ Unblocks and removes emotional stressors that block creative energies
♦ Connected to sexuality, fertility and reproduction.
Tetrahedron
♦ Fire Element
♦ Solar Plexus
♦ Key Function: manifestation
♦ 3rd Dimension
♦ Sits flat no matter which side, perfect symbol for balance and stability
♦ Balance between the physical and spiritual
♦ Supports personal power and acceptance
♦ Creates change.
Octahedron
♦ Air Element
♦ Heart
♦ 4th Dimension
♦ Key Function: integration
♦ Cultivates acceptance, forgiveness, love and compassion for self and others
♦ Its mirroring or self-reflecting shape moves us to a higher vibration of reflection, compassion and healing – As Above, So Below.
Dodecahedron
♦ Ether Element
♦ Third Eye, Crown and Higher (8th and above) Chakras
♦ Key Function: ascension and mystery
♦ Represents divine creation associated with the Universe
♦ Holds a very high but gentle energy so helps cultivate a higher vibration in meditation
♦ An expression of life & consciousness beyond physical vibrations of the body
♦ Connect to Higher Self or Source energy.
Crystals and the Platonic Solids
Platonic Solids often come in boxed crystal sets, and in particular they can be made of the following healing crystals:
♦ Clear Quartz - clarity, channelling, amplifying energy and thought, assisting with creating power.
♦ Rose Quartz – enhancing all forms of love, opening the heart, peace, calming, nurturing, balancing emotions, teaching forgiveness and tolerance.
♦ Amethyst – spiritual awareness, meditating, balance, psychic abilities, inner peace, healing of body, mind and spirit.
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. When Platonic Solids with their high energy field are introduced into a weaker or chaotic energy field, such as when humans are ‘stuck’ or become ill or emotionally unbalanced, they can re-harmonise, realign and restore the energetic vibration. Healing can then occur on the mental, spiritual, emotional and/or physical levels.
Summary
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.