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Merkaba: everything you've never been told 
3 good reasons to put a suncatcher in your house Platonic solids: symbols of perfection
The Platonic Solids come from Sacred Geometry, a Pythagorean tradition transmitted to Plato during his teaching at the Academy, where he studied under the tutelage of his mentor, Speusippus. Plato, successor to Socrates, deepened this mathematical and philosophical knowledge, the foundations of which go back to ancient Greece and mathematicians like Theaetetus of Athens.
These solids, also known as convex regular polyhedra, have remarkable properties. They can all be inscribed in spheres, and their faces, edges and angles are equal. This regularity makes them particularly significant in the representation of shapes and structures in the universe.
Among the Solids, two of them, the dodecahedron and the icosahedron, are not described in Plato's early writings. On the other hand, they are attributed to Archytas of Tarentum, a Greek mathematician and philosopher contemporary of Plato.
Greek mathematicians studied these shapes in depth. This allowed them to discover important relationships between them, such as the sum of face angles and Euler's formula. Even more, these solids are linked to the notion of the Golden ratio, the mathematical proportion which is considered aesthetically harmonious.
Each shape has very interesting properties that I invite you to discover in this article.
Shall we go?
Who invented the Platonic solids?
Platonic solids are not strictly "invented" by Plato himself. They were discovered and studied by Greek mathematicians long before Plato's time, but Plato made them famous in his philosophical dialogues, especially in his work called "Timaeus".
The Solids are named after Plato because it was he who described them and made them popular in his writings. However, it would seem that their study dates back well before Plato, to the Greek era of Pythagoras and his disciples.
What are the Platonic solids? Why 5 Platonic solids?
Solids play a determining role in Plato's philosophy. The Greek philosopher, in the dialogue Timaeus (c. 358 BC), associated each of the four elements (earth, air, water and fire) with a regular solid. These five solids have the particularity of being regular polygons, that is to say figures with several faces which can fit into a circle and all of whose vertices (corners) are in contact with the circle.
Names, properties and symbolism of the Platonic solids
Plato considered these 3D polygons to be perfect, and gave names and definitions to five of them:
| Element | Platonic solid | Number of edges | Number of plans | Number of faces | Number of vertices | Shape of each side |
| Ether | Dodecahedron | 30 | 60 | 12 | 20 | Pentagon |
| Fire | Tetrahedron | 6 | 12 | 4 | 4 | Triangle |
| Air | Octahedron | 12 | 24 | 8 | 6 | Triangle |
| Water | Icosahedron | 30 | 60 | 20 | 12 | Triangle |
| Earth | Hexahedron (or cube) | 12 | 24 | 6 | 8 | Square |
These five polyhedra played a pivotal role in both practical and mystical realms of geometry, although it's worth noting that Plato wasn't the first to delve into their mysteries. The first three belong to Pythagoras, while the last two can be credited to Theaetetus, dating back to the 4th century BC.
Among the vast multitude of shapes composed of irregular polygons, only five stand out as being constructed entirely of regular polygons.
This remarkable singularity led both Aristotle and Plato to regard these figures as the elemental building blocks of the physical world, associating them with the classical four elements, to which they added a fifth, known as ether (Aether in Latin).
The term "polyhedron" simply refers to a three-dimensional shape composed of symmetrical, multi-faceted surfaces.
Despite their intricate appearances, these solids are actually elegantly simple:
- The cube, a quintessential rectangular form, reigns as the most fundamental and regular among them.
- The tetrahedron takes the shape of a pyramid with a triangular base.
- The octahedron comprises two identical pyramids with square bases, seamlessly joined.
Each of these solids carries its own inherent virtue, akin to the symbols of sacred geometry.
The tetrahedron, aligned with the element of fire, embodies an active force, symbolizing emergence and ascension. The unique shape of the tetrahedron can bolster overall well-being and amplify intentions, proving effective in combating severe fatigue or expediting recovery.
The hexahedron, grounded in the element of earth, represents a steadfast and stable essence. Its shape's vibration promotes stability, precision, and security. It fosters adept management of the material world and, consequently, the sustenance of the physical body.
The octahedron, associated with the element of air, exudes subtlety and exchange in all directions and dimensions. It enhances subtlety and lightness in our psychic environment while strengthening the aura.
The icosahedron, linked to the element of water, champions fluidity, dissolution, and purity. It has the power to open the heart chakra, facilitating a connection with our causal soul. This shape is particularly adept at dissolving barriers, enabling the flow of affection and love towards others, and transforming our vibrational emissions to reshape our lives.
The dodecahedron, representing the element of ether, symbolizes the fifth element, an ethereal energy underlying the four classical elements. It serves as a catalyst for our spiritual development, fostering a connection with our spiritual soul and our unique life purpose.
Platonic solids and the elements
The five solids form two groups of elements: duals on the one hand, and ether on the other. The cube (earth) and the octahedron (air) are geometrically dual, meaning that one can be created inside the other by connecting the points marking the center of each face. A cube can therefore be built inside an octahedron, and vice versa, ad infinitum.
Similarly, the other two elements represented by the tetrahedron (fire) and the icosahedron (water) are dual and can generate each other.
There is therefore perfect symmetry between each pair of elements, earth-air and water-fire. The dodecahedron is dual in itself, so ether can generate itself.
So, to sum up:
Plato links the solids to the great entities he believed shaped the world: fire, air, water, earth and ether.
Each is linked to an element of Creation:
- Plato's 1st solid: the Tetrahedron: fire
- Plato's 2nd solid: the Octahedron: air
- Plato's 3rd solid: the Icosahedron: water
- Plato's 4th solid: the Cube: earth
- Plato's 5th solid: the Dodecahedron: represents the Whole, the Universe
The solid sphere
The sphere is really the perfect volume where every point on the surface is at an equal distance from the center and where all the pressures exerted on its surface are in equilibrium, which gives it its shape (like a drop of liquid in weightlessness).
Around 70-80% of us are made up of water, and this element is symbolized by the sphere, the drop, the lake, the waves - it speaks to us internally.
The sight of a sphere immediately puts us in resonance with our planet, the celestial bodies, the stars and the cosmos. The sun and moon have been deified for millennia. As such, they have remained symbols of perfection in the collective unconscious.
The sphere radiates and harmonizes the space around it up to a distance proportional to its size. The use of a crystal sphere as a re-harmonizer is very common in Feng Shui and geobiology. It's a good tool for restoring a satisfactory overall vibratory rate.
Don't hesitate to take a look at our collection of crystal suncatchers.
Getting back to the crystal ball, we're all familiar with its use in clairvoyance and mediumship, but it's also a good tool for meditation.
Platonic solids and the Merkaba in lithotherapy
The star polyhedron now known as the Merkaba is made up of two tetrahedrons. This is why it's called the tetrahedral star.
The Merkaba is defined by the essence of its name. According to Egyptian terminology, it's made up of three words: MER, the celestial light, KA, the energetic body, and BA, the incarnated soul. The word Merkabah (or Merkavah) is therefore an Egyptian term, then a Hebrew one.
In the Kabbalah, it took on the meaning of vehicle or chariot and was associated with the inner journey. Jewish mysticism and kabbalah have their origins in ancient Egypt.
Compared to an energetic vehicle, the Merkaba can help our body, mind and soul to access and experience other levels of consciousness or life potential.
A Merkaba crystal appears as a star tetrahedron; a three-dimensional 8-pointed star composed of two triangular pyramids, one pointing upwards, the other downwards. It was appreciated and used in many cultures and religions, including the ancient Egyptian and Jewish ones.
A Merkaba crystal is an effective tool that can be used in many different ways to help you reach your full potential. It can be composed of different crystals with powerful healing and energetic cleansing properties.
Used in meditation, a Merkaba crystal enables you to experience expanded consciousness, connecting you with your higher self and helping you to experience heightened states of awareness.
Performed correctly, Merkaba meditation integrates and harmonizes the feminine and masculine aspects of your being.
A Merkaba crystal can be programmed through meditation and intention.
Merkaba crystals can also be used:
- In advanced Reiki practices
- To travel in the astral realms
- To activate and purify the human Light Body
- For Mer-Ka-Ba visualizations
Platonic solids in history
The antiquity of solid objects is remarkable.
Among the Neolithic communities of Scotland, hundreds of meticulously carved stone spheres, approximately three inches in diameter, have been unearthed, believed to trace back to roughly 2000 BC. Intriguingly, some of these spheres bear etched lines that align with the edges of regular polyhedra. While approximately half of these spheres exhibit six distinct knobs, others display a diverse range of knob counts, spanning from three to an astonishing 160.
Plato's solids are ancient, found in excavations dating back hundreds of years. Like these ancient Roman and Egyptian excavations (200 - 400 AD). They used the dodecahedron and icosahedron, probably as dice. Their true purpose remains a mystery.
The initial discovery of a dodecahedron took place in 1739, and since then, researchers have uncovered at least 116 similar objects across various regions, spanning from Wales to Hungary and Spain to eastern Italy, with the majority located in Germany and France. These dodecahedra vary in size, ranging from 4 to 11 centimeters in diameter.
In ancient Greece, these five solids held a special significance, serving as fundamental models for the physical world. Four of these solids were associated with the archetypal representations of the four classical elements (earth, air, fire, and water), while the fifth solid stood as the model representing the life force itself, known as ether in Greek philosophy.
These geometric forms also featured prominently in the numerous prehistoric carved petrospheres discovered in Scotland. Surprisingly, more than 75% of these petrospheres depicted one of Plato's five solids, originating from a time more than a millennium earlier than ancient Greek civilization. It is now recognized that these same shapes bear a profound connection to the spatial arrangements of protons and neutrons within the elements listed in the periodic table.
Euclid and the five Platonic solids
Euclid, in his renowned work "Elements" around 300 B.C., provided a comprehensive mathematical exposition of Plato's solids. The final book, Book XIII, is dedicated to delving into their properties. Within this book, Propositions 13 to 17 meticulously elucidate the construction of the tetrahedron, octahedron, cube, icosahedron, and dodecahedron, presented in that precise order.
For each of these solids, Euclid masterfully determines the ratio between the diameter of the circumscribed sphere and the length of their edges. Proposition 18, a pivotal point in his exploration, argues convincingly that there are no additional convex regular polyhedra to be found. This assertion is grounded in the fundamental principles of regularity in polyhedra, namely, that a regular polyhedron must boast an identical number of regular polygons at each of its vertices, and furthermore, the sum of angles at the vertices of these regular polygons must remain strictly less than 360°.
Luca Pacioli (1147-1517)
Luca Pacioli was a man of diverse interests and talents. As a Franciscan monk and mathematician, he formed a close friendship with Leonardo da Vinci, leading to their collaborative efforts. Pacioli also held teaching positions in various Italian cities.
One of his significant achievements was the publication of a Latin edition of Euclid's Elements. However, his most renowned work, "Summa di arithmetica, geometrica, proportione et proportionalita," published in 1494, can be aptly described as a comprehensive mathematical encyclopedia that catapulted him to fame.
In 1509, Pacioli published "De Divina Proportione" in Venice, a manuscript he had offered to Ludovico le More, Duke of Milan, several years earlier. This work, featuring illustrations by Leonardo da Vinci, primarily delves into the study of the properties of divine proportion. Additionally, it includes a concise treatise on architecture, the exploration of an ancient alphabet, and the "Libellus," a collection of mathematical exercises, notably focusing on regular polyhedra.
When Pacioli studied the Golden Number in this work, it was no longer, and had long been, an unknown number to mathematicians. In fact, its definition closely follows that given by Euclid.
Johannes Kepler (1571-1630)
Johannes Kepler, much like Pythagoras (c. 580-495 BC), possessed a profound appreciation for mathematics and perceived its presence in all aspects of the world, whether it be in the vibrations of a stringed instrument or the intricate motions of celestial bodies, particularly the planets.
Kepler's interests extended beyond the realm of conventional science, delving into mysticism. In his 1596 work "Mysterium Cosmographicum" (The Cosmographic Mystery) and later in his 1619 treatise "Harmonices mundi" (The Harmony of the World), he ventured into the idea of the Universe as an intricately harmonious arrangement of geometric forms.
In "Mysterium Cosmographicum," Kepler unveiled a novel model of the solar system. Within this model, he ingeniously nested the five Platonic solids, arranging them one within the other, and interspersed them with a series of inscribed and circumscribed spheres.
This German astronomer's quest also led him to explore potential connections between the five planets known during his time (excluding Earth) and Plato's quintessential five solids, unveiling fascinating links between geometry and celestial motion.
Kepler put forth the intriguing proposition that the proportional distances between the six planets known during his era could be comprehended by interlacing Plato's five solids. Each of these solids was encapsulated within a sphere, symbolizing the orbit of a particular planet, with the outermost sphere representing the orbit of Saturn.
In pursuit of his vision, Kepler crafted a theory centered around regular polyhedra to construct a model of the Universe. Notably, he discerned that the five Platonic solids could be seamlessly nestled between the "orbs" (with an "orb" here referring to a spherical structure, or more precisely, a hollowed-out globe that encompasses the path of a celestial body) of the six known planets, ranging from Mercury to Saturn. This insight showcased Kepler's profound ability to connect geometry and the celestial movements of the heavenly bodies.
These regular polyhedra, being geometric shapes of unparalleled symmetry, closely approached the divine perfection inherent in the sphere. Employing them in the construction of the solar system was a testament to the majestic nature of divine creation itself.
The quantity of these polyhedra held a direct correlation with the number of planets, marking five intervals and consequently accoun ting for six planets. However, their arrangement within the system also offered insight into the proportions governing the planetary orbits, specifically the relative distances between the planets and the Sun. Each polyhedron was elegantly inscribed within the orbital path of one planet while simultaneously being circumscribed by the orbital path of the planet immediately adjacent. This interlocking arrangement unfolded as follows: the cube nestled between the orbits of Saturn and Jupiter, the tetrahedron fitting within the gap between Jupiter and Mars, the dodecahedron positioned between Mars and Earth's orbit, followed by the icosahedron encompassing the path of Venus, itself encircled by the octahedron, which, in turn, enveloped the orbit of Mercury.
It is worth noting that Kepler's original hypothesis did not ultimately hold true, but this did not deter his relentless pursuit of understanding the universe. Through his continued research, he arrived at groundbreaking discoveries, including the revelation of Kepler's solids, the recognition that planetary orbits are not perfectly circular, and the formulation of Kepler's laws of planetary motion, which have since secured his place as a revered figure in the annals of science.
Platonic solids in nature
The tetrahedron, cube and octahedron all appear naturally in crystal structures. These by no means exhaust the number of possible crystal shapes. However, neither the regular icosahedron nor the regular dodecahedron are among them.
One of these forms, called the pyritohedron (named after the group of minerals with which it is typical) has twelve pentagonal faces, arranged in the same pattern as the faces of the regular dodecahedron. However, the faces of the pyritohedron are not regular, so the pyritohedron is not regular either.
Circogonia icosahedra, a species of radiolaria, shaped like a regular icosahedron.
In the early 20th century, Ernst Haeckel described numerous species of radiolaria, some with skeletons in the shape of various regular polyhedra. His examples include Circoporus octahedrus, Circogonia icosahedra, Lithocubus geometricus and Circorrhegma dodecahedra, the shapes of these creatures being obvious from their names.
Many viruses, such as the herpes virus, are shaped like a regular icosahedron. Viral structures are built on identical repeated protein subunits, and the icosahedron is the easiest shape to assemble using these subunits. A regular polyhedron is used because it can be built from a basic protein unit used indefinitely, thus creating space in the viral genome.
How to use and place the 7 Platonic solids in rock crystal?
How to use a dodecahedron?
The dodecahedron is the fifth Platonic solid. It is particularly recognized as being the representation of the universe as a whole or as a symbol of perfection.
This fifth solid is a regular convex polyhedron composed of twelve identical pentagonal faces. In mathematics, its study allows you to understand the properties of geometry in three-dimensional space, as well as mathematical concepts such as the geometry of solids, angles and proportions.
In divination, some practitioners use specially marked dodecahedrons for divination or meditation. Each face can represent a concept, an element or a direction. It can be used as a thinking or decision-making tool.
Platonic solids and the chakras
Just as each Platonic solid harmonizes with one of the fundamental elements, each of these elements in turn resonates with a specific chakra within our energy system. This interconnectedness underscores the notion that all aspects of existence are intricately linked.
As famously articulated by Leonardo da Vinci: "Recognize that everything is interconnected with everything else."
Every facet of existence exerts an influence on all others. Therefore, if a blockage manifests within any of your chakras, its repercussions will extend to affect the entirety of your being.
The activation of these Platonic solids can be harnessed within the human body to yield several benefits, including:
- Reawakening cellular awareness.
- Releasing latent cellular memories.
- Elevating the vibrational frequency, thereby augmenting the potential for self-healing on physical, emotional, or mental planes.
- Rehabilitating the structure and fortitude of the human light body.
Reclining for a span of 40 minutes, with your head oriented to the north, embark on the installation of these geometric solids (you can seek assistance if needed). Alternatively, proceed methodically through the following steps:
- Begin by selecting the Cube and position it in close proximity to your perineum, associated with the 1st chakra.
- Gently place the Cube aside and take up the Icosahedron. Position it near your lower abdomen, linked to Chakra 2.
- Set the Icosahedron aside and pick up the Tetrahedron. Place it in the vicinity of your solar plexus, corresponding to Chakra 3.
- Following that, rest the Tetrahedron and acquire the Octahedron. Situate it near your heart chakra, denoted as Chakra 4.
- Place the Octahedron aside and grasp the Dodecahedron. Position it in proximity to your throat chakra, aligned with Chakra 5.
- Shift the Dodecahedron closer to your 3rd eye chakra, corresponding to Chakra 6.
- Finally, place the Dodecahedron near your coronal chakra, associated with Chakra 7, and allow it to rest.
At each stage of this re-harmonization journey, every solid will emanate distinct vibrational frequencies.
The dodecahedron represents the element ether and it symbolizes the crown chakra. It acts on the mind and its emotions in order to release them. It strengthens the will. And placing a dodecahedron near you during the night harmonizes sleep.
The hexahedron represents the earth element and it symbolizes the root chakra. It acts on the balance of fugitive and evanescent people by promoting rooting.
The icosahedron represents the element water and it symbolizes the sacral chakra. It acts on mental turbulence by calming instability. It helps to better self-manage sexuality.
The octahedron represents the air element and it symbolizes the heart chakra. It acts on emotional memories by bringing balance, calming and love. It develops and strengthens respect for oneself and others. It helps with expression and syntax.
The tetrahedron represents the element fire and it symbolizes the solar plexus chakra. It acts on all subtle bodies by readjusting the alignment between heaven and earth, by untying energetic knots. It develops the ability to resolve a dilemma.
Using Platonic solids for spiritual growth
There are numerous ways to harness the spiritual potential of Platonic solids, with meditation being a particularly common approach. When you engage with these Platonic solids, you are essentially tapping into the energies of creation itself. This practice allows you to manifest a new life that is more harmonious with your true self, aligning your existence with your higher purpose.
This, in essence, is the profound spiritual significance of Platonic Solids.
Beyond active utilization, Platonic Solids exert a subtle influence on our subconscious, much like other forms of Sacred Geometry. By merely placing these objects within a room, they act as harmonizers, balancing the energies within that space.
Each Platonic Solid possesses its unique ability to harmonize energies that resonate with its inherent properties.
Here, let's delve into the spiritual meanings of these Platonic Solids and explore how each one can be employed for spiritual growth:
1. The Spiritual Meaning of the Cube (Hexahedron):
The Cube primarily serves as a grounding force. It facilitates a reconnection with the Earth's energies and nature, firmly anchoring you in the present moment. Some even believe it has the potential to activate Kundalini energy. This Platonic solid is especially beneficial in reducing stress and alleviating physical tension. Moreover, it provides a stable foundation for creativity, serving as the bedrock upon which creative inspiration thrives.
2. The Spiritual Significance of the Icosahedron:
The Icosahedron excels in the realm of transformation. It enhances creative thinking and assists in breaking through emotional blockages that hinder creative energies. This solid encourages you to embrace a new way of life, promoting freedom of expression, creativity, and positive change. It fosters an understanding of your emotions, helping you navigate and respond to them. The Icosahedron is a valuable tool for achieving balance and harmony, particularly in matters related to fertility and sexuality.
3. The Spiritual Meaning of the Tetrahedron:
The Tetrahedron's primary function is manifestation. It empowers you to effect change in your life, supporting personal growth and acceptance of the old to make way for the new. This solid enhances clear thinking and illuminates certain ideas. It symbolizes the balance between the physical and spiritual realms and is regarded as a symbol of equilibrium and stability.
4. The Spiritual Significance of the Octahedron:
Integration is the central role of the Octahedron. It aids in healing, acceptance, forgiveness, and compassion, both for yourself and others. The Octahedron facilitates reflection and elevates your vibrational frequency. It encourages self-compassion, catalyzing the healing process. This solid also promotes creative self-expression and heart-centered communication, fostering a deeper connection between your inner and outer worlds.
5. The Spiritual Meaning of the Dodecahedron:
The Dodecahedron embodies ascension, expression, the divine creation of life, and the highest realms of consciousness. It elevates your vibrational frequency, facilitating a connection with higher dimensions and your higher self. This solid serves as a potent tool for meditation, resonating at a very high frequency that not only elevates your own energy but also that of your environment.
Plato's solids in geobiology
Activating the solids in geobiology enables you to treat:
- Electromagnetic pollution
- The various telluric or cosmic-telluric networks (Curry, Harthman)
- Underground springs
- Wall memories, presence of entities
They are formidable allies in harmonizing and protecting living and working spaces.
How else can you work with Plato's solids?
You can wear an extra rock crystal solid as a pendant.
You can place a crystal solid in your drinking water to inform it and integrate this information when you drink it (remember to clean your solid beforehand, on a Fleur de Vie harmonizing disc for example).
You can place a (slightly larger) crystal solid in your home or office, to re-harmonize the space. You can select the solid according to your choice and what you wish to transform.
You can also use Platonic solids in radionics, to emit beneficial information at a distance to ourselves or another person.
A final word
The search for regularity and harmony is an ancient quest of the human spirit.
Plato's solids, or regular polyhedra, permeate many aspects of our world. They appear in crystals, in the skeletons of microscopic marine animals, in children's toys and in art. They have been studied by philosophers and scientists such as Plato, Euclid and Kepler. They are of great interest to classical geometry, as Euclid's work focuses on the figures themselves. They also play a very interesting role in modern geometry.
In fact, no new convex regular polyhedra has been discovered since Euclid. In fact, it can be shown that there are only 5!
We've come to the end of this article. I hope you've enjoyed it, so please feel free to comment, share and subscribe to our newsletter to be informed of future releases.
And if you'd like to take your symbol discovery one step further, welcome to this space/shop dedicated to sacred geometry. Here you'll find a multitude of fractal mandalas.
Sources :
Géométrie sacrée, Éditions Véga
Le pouvoir des symboles, Éditions Trajectoire
https://fr.wikipedia.org/wiki/Johannes_Kepler
