A foundational aspect in the study of sacred geometry lies in five basic three-dimensional shapes, which are called the platonic solids. Indeed, for those who believe in sacred geometry, all physical matter is fundamentally linked to these shapes. Thus, the platonic solids are referred to as the “building blocks” of the Universe itself. In this post, we’ll explore the platonic solids, from how they appear in nature, science, art, and architecture, as well as their connection to spirituality and other aspects of our existence.
Table of Contents
While the 5 platonic solids are unique shapes, they all share the following key characteristics:
The five platonic solids are the:
1. Tetrahedron – 4 faces
2. Cube, or hexahedron – 6 faces
3. Octahedron – 8 faces
4. Dodecahedron – 12 faces
5. Icosahedron – 20 faces
What’s important to keep in mind as we study the platonic solids is that all physical matter is simply a dense manifestation of energy.1 So, as we exist on Earth, studying these shapes helps us to grasp concepts that are actually beyond the material realm. Everything is energy. Thus, sacred geometry patterns are crystallized forms that can help us envision a higher reality.
While they’re named for the Greek philosopher Plato, the platonic solids were studied by people even before Plato’s time.
For one, the ancient Egyptians were a spiritually enlightened people who likely understood the notion that the Universe was formed by fundamental building blocks.
The Egyptians’ knowledge then influenced the 6th century BCE philosopher and mathematician Pythagoras (who some say was the great grandfather of modern-day numerology.) Pythagoras had a strong influence on Plato, and both believed that the secrets to the Universe could be understood by numbers and mathematics.
At the same time, archaeological evidence from other parts of the world hints that other ancient peoples believed that simple shapes held the keys to universal understanding.
Carved stone balls used for divining and other purposes from the Neolithic Period, ca 3200 BCE. Source: Kelvingrove Art Gallery and Museum. Image: Johnbod.For example, carved stone balls that date back to the Late Neolithic Period, or approximately 5,200 years ago, have been discovered in Scotland, Britain, and Ireland. One of the uses of these balls was to interpret messages from the gods or to get an answer to a question based on how the ball landed after being tossed. The theory was that the ball was influenced by metaphysical energetic forces.2
It was round 347 BCE that Plato fine-tuned the theory that the five platonic solids were fundamental constituents of the physical world. In fact, Plato connected the platonic solids to what the Greeks believed at the time to be the key five elements of Earth.
The ancient Greeks believed that five elements made up the world, and that each of the platonic solids was the embodiment, or physical representation, of each element.
The platonic solids appear throughout the Universe in fascinating ways. For example, they appear in intriguing ways in nature. (It’s important to note, however, that in nature, perfect symmetry is rare.) The following are ways the platonic solids appear in nature. We’ll go into more detail on some of these in the section on science below.
Molecular Structures: A methane molecule (CH₄) displays atoms that are positioned at the corners of a tetrahedron, with carbon at the center and hydrogen atoms at the vertices.
Mineral Crystals: Certain crystals, like pyrite, can sometimes form tetrahedral shapes. In addition, diamonds and fluorite can form natural octahedral crystals. These crystals are a result of the atomic structure and growth conditions of the minerals.
Crystalline Structures: Common salt (NaCl) crystallizes in a cubic formation. The cubic crystal structure is also seen in minerals like pyrite and halite.
Biological Structures: Some viruses approximate an octahedral symmetry in their capsid structures (though it’s not perfect symmetry.) In addition, while the dodecahedral shape is rare in nature, it can be observed in some microscopic structures, like certain radiolarians, a type of plankton.
Meteorology: In rare instances, dodecahedral shapes have been observed in the formation of high-altitude cloud formations known as skylons.
Viral Structures: Many viruses, including the common cold, have icosahedral capsid structures.
Microscopic Organisms: Certain radiolarians also exhibit icosahedral symmetry.
Also, in nature, the platonic solids appear in fascinating ways on the Earth itself. For example, the 16th century German Renaissance man, Johannes Kepler (who inspired the development of the Kepler map), wrote extensively about the geometrical basis of the Universe.3
Kepler linked the platonic solids to the solar system. He proposed a model whereby the solids were nested inside one another. Each one was enclosed by a sphere representing the orbits of the six planets known in his time.4 Saturn’s orbit was the outermost sphere.
Kepler observed that the distances of these planetary orbits bore a striking resemblance to the ratios of the sizes of the spheres surrounding each platonic solid. Although later proven inaccurate, this model was a significant step in astronomical research, leading to Kepler’s more precise laws of planetary motion. His theory symbolized a historical attempt to find a geometric order to the cosmos.
It wasn’t until the late 1960s, however, that Ivan Terence Sanderson, a British biologist, writer, and naturalist, made an intriguing discovery about the geometric locations of physical anomalies on the Earth.
Sanderson found that regions on Earth where (what he and others believed) a disproportionate number of strange phenomena occurred, such as disappearances and UFO sightings, were spread equally in 12 sections. The sections are over the Tropic of Cancer and the Tropic of Capricorn and include the North and the South Poles. Sanderson found that the assortment of these locations on Earth formed the nodal points of the geometric shape of the platonic solid that is the icosahedron (if it was laid out in two dimensional form.)
These locations – which are unfortunately nicknamed “The Vile Vortices” – include:
Researchers discovered that Earth grid maps, such Sanderson’s icosahedron, could align properly into sacred geometry patterns if the starting point of the grid was aligned with the Giza Plateau in Egypt, where the Great Pyramid of Giza is located. For believers in sacred geometry, the location of the Great Pyramid is in one of the Earth’s chakras, or key energy centers.6
The platonic solids are not only seen in the natural world, they’re also prevalent in mathematics. Here are some examples:
Geometric Symmetry: In mathematics, the platonic solids are special geometric shapes because of symmetric structure. As mentioned earlier, each solid is made up of faces that are congruent regular polygons. And the number of faces meeting at each vertex is the same across the solid. This uniformity and symmetry make them an important object of study in geometry.
Euler’s Formula: A remarkable aspect of the platonic solids in mathematics is their connection to Euler’s formula. This formula, V – E + F = 2 (where V is the number of vertices, E is the number of edges, and F is the number of faces), is valid for all platonic solids. This relationship is a cornerstone in the study of polyhedra and topology.
Dual Solids: Each platonic solid has a dual (or polar) solid, where the vertices of one correspond to the faces of the other. For example, the cube and the octahedron are duals. This concept of duality is a fascinating topic in geometry, offering insights into the interconnectedness of these forms.
Applications in Higher Mathematics: Beyond their geometric properties, the platonic solids find applications in various fields of higher mathematics, such as group theory and combinatorics. They are fundamental in the study of symmetry groups, known as polyhedral groups, which are key in understanding spatial symmetries.
In addition to mathematics, the platonic solids appear in scientific study. For example:
The physicist Dr. Robert J. Moon (1911 – 1989) proposed a new way of looking at atoms based on the platonic solids. He was inspired by Johannes Kepler’s theories about these fundamental shapes.
Dr. Moon theorized that in an atom, protons (the tiny particles in the atom’s center) are not just floating around in the middle. But rather, they sit at the points of a 3D shape. He imagined atoms as being made up of layers, each with a different number of protons at their corners.
Dr. Moon suggested that at the center of this model is a cube shape. This represents an oxygen atom, which has 8 protons. Surrounding this cube, he placed an octahedron shape, adding 6 more protons for a total of 14, representing a silicon atom.
According to Dr. Moon, every element in the periodic table can be described using a combination of the platonic solid shapes. When atoms join together to make molecules, and those molecules form crystals, these geometric shapes become even more apparent. This idea suggests that all matter is made up of these basic geometric forms.7
Here are some specific ways the platonic solids appear in science:
Chemistry: In chemistry, the platonic solids appear in the molecular structure of certain compounds. For instance, as mentioned earlier, the tetrahedral shape is fundamental in the molecular geometry of many compounds, such as methane (CH₄). This configuration is crucial for understanding the chemical bonding and reactivity of these molecules.
Physics: In physics, notably in crystallography, the platonic solids help in understanding the shapes and structures of crystals. For example, as mentioned earlier, natural crystals, like pyrite and fluorite, often form shapes that resemble octahedrons, which helps scientists who study crystal growth and properties.
Biology: In biology, particularly in virology, the icosahedral shape is evident in the structure of various viruses. This geometric form is used by viruses for creating a robust yet efficient capsid to house their genetic material, a fascinating example being the common cold virus.
Geology: In addition to what has been mentioned earlier, geologists observe the platonic solids in the study of certain mineral crystals. The cubic form, for example, is clearly seen in the crystalline structure of common salt (NaCl) and pyrite. Understanding these structures is key to comprehending the formation and physical properties of these minerals.
Environmental Science: In the study of meteorology and environmental science, the platonic solids occasionally make an appearance in natural phenomena. For example, certain high-altitude cloud formations, known as skylons, have been observed to take on dodecahedral shapes, although this is rare.
As art reflects the way we experience the world, the platonic solids naturally appear throughout the art world. Here are just a few examples:
Leonardo da Vinci: Divina proportione, which means the Divine proportion, is a book on mathematics that was written by Luca Pacioli in 1497-1498. It was meticulously illustrated by Leonardo da Vinci. The book covered geometric mathematical proportions, including the Golden Ratio, and their applications in art and architecture. da Vinci’s illustrations were so popular that they had a strong influence on the art and architecture of the period.
M.C. Escher: M.C. Escher (1998-1972) was a Dutch artist who was fascinated by the regular solids, known as polyhedra. He made them the subject of many of his works. His print “Stars” features all five of the platonic solids and the rhombic dodecahedron.
George Hart: Sculptor George Hart’s work explores the interplay between mathematics and art. He uses materials like wood and metal to construct intricate three-dimensional representations of these shapes. The platonic solids can be seen throughout his artwork.8
Drew Brophy: Surf artist Drew Brophy incorporates the platonic solids in many of his paintings. He has written about the symbolism and meaning behind these shapes, and how they relate to his art.9
Joanie Lemercier: JoanieLemercier is a visual artist and environmental activist whose work explores human perception through the manipulation of light in space. His collection “Platonic Solids: The Elements” features stunning visual representations of this subject.10
The platonic solids, with their perfect symmetry and balance, have also inspired the world of architecture for centuries. These geometric forms serve not just as aesthetic elements but also as structural components, bringing together artistry and engineering.
Here are just a few examples of the platonic solids in architecture:
The Great Pyramids of Egypt: Perhaps the most ancient and iconic example of the platonic solids in architecture is the Great Pyramids of Egypt, in particular, the Pyramid of Khufu at Giza. This pyramid, often associated with the shape of a square pyramid (a variation of the tetrahedron), demonstrates the ancient Egyptians’ profound understanding of geometric principles.
All of the pyramids’ precise alignment with the cardinal points and their proportional dimensions reflect a deep knowledge of spatial geometry. These architectural marvels are not only burial places but also symbols of the Egyptians’ astronomical and mathematical prowess, embodying the platonic ideal of harmony and cosmic order.
The Eden Project: In Cornwall, England, the Eden Project’s geodesic domes showcase how hexagons and pentagons (elements of the platonic solids) can create a complex, self-supporting structure. These domes, housing vast botanical gardens, are a testament to the harmony between architecture, nature, and sacred geometry.
The Atomium: Designed for the 1958 Brussels World’s Fair, the Atomium is an awe-inspiring structure resembling a unit cell of an iron crystal magnified billions of times. Its spheres and connecting tubes create an octahedral shape, offering a unique blend of scientific concept and architectural innovation.
The Tomb of Gömeç Hatun: The platonic solids appear throughout Islamic architecture and design. For example, you can see them in intricate tile work and muqarnas, or decorative vaulting.
Notably, the Tomb of Gömeç Hatun Konya, Turkey which dates back to the 13th century, is an example of a dodecahedron covered with intricate geometric patterns. The use of these shapes in Islamic architecture symbolizes the perfection and unity of the Universe.11
The platonic solids also appear in various religious and spiritual beliefs in which they often symbolize fundamental concepts about the Universe and creation. Here are some examples:
Ancient Greek Philosophy: As referenced earlier, Plato believed the platonic solids were evidence of a divine plan by a single creator. While the Greeks were staunch proponents of science and mathematics, they also held spiritual beliefs about metaphysical powers that were stronger than those of human beings.
Christianity: In Christian symbolism, the platonic solids represent the existence of a divine plan by a single creator. In addition, they are emblematic of the perfection of God’s creation and a harmony to the order of the Universe.
Hinduism and Buddhism: In Eastern religions, such as Hinduism and Buddhism, some of the platonic solids appear in mandalas and yantras. These designs are geometric representations of the Universe’s structure, serving as tools for meditation and contemplation.
Esotericism and Occultism: In esoteric traditions and occult practices, the platonic solids are sometimes used as symbols of hidden knowledge or mystical truths. Believers say they hold key insights into the fundamental principles of the cosmos and the spiritual realm.
Astrology: Plato believed that the dodecahedron symbolized the ideal and eternal forms that underlie the physical world. He also believed that each of the faces on the 12-faced dodecahedron represented a celestial region and, therefore, a zodiacal sign.
New Age Spirituality: In New Age spiritual beliefs, the platonic solids are associated with various energy frequencies and healing properties. For example, practitioners use them in crystal healing. They also use different solids based on their vibrational properties in chakra work.
As the platonic solids have their own vibrational frequency, practitioners used them in healing and meditation practices. For example, as referenced earlier, each solid corresponds to a specific chakra, symbolizing the qualities and elements associated with it.
For example, the stable and grounding cube resonates with the root chakra, which is the foundation of your security and primal energy.
In addition, the flowing and dynamic icosahedron represents the sacral chakra. This governs your sexuality, social connections, sense of movement, and creative flow. You can see how these associations highlight a fascinating blend of geometry and energy work, emphasizing the balance and flow of life forces within the body. Essentially, this is how energy healing vibrational medicine works.
Furthermore, Plato associated the dodecahedron with ether. For the Greeks, ether was the element of the metaphysical, or godly realm. Thus, the dodecahedron is connected to both your third eye chakra and your crown chakra.
Each platonic solid resonates with specific energies and attributes, which you can harness in the practice of meditation and manifestation. In your practice, you can visualize the solids and meditate them. You can also use them in their physical forms, such as crystals and figurines. In essence, their geometric perfection can help you to focus and to amplify your intentions in a way that harmonizes with universal frequencies.
Each solid has its own special properties and potential uses:
Tetrahedron (Fire): Representing the element of fire, you can use the tetrahedron symbol to manifest change, passion, and transformation. It may help in focusing energy towards initiating new projects or igniting creativity.
Cube (Earth): Representing the material world and stability, the cube is ideal for manifesting material abundance, security, and physical well-being. It can be a tool for focusing on career goals, financial stability, stable relationships, or health improvements.
Octahedron (Air): Associated with the air element, the octahedron aids in manifesting mental clarity, communication, and intellectual growth. It’s useful for goals related to learning, resolving conflicts, or enhancing social connections.
Icosahedron (Water): Associated with water and flow, the icosahedron resonates with emotions, intuition, and being in flow. It’s beneficial for manifesting emotional healing, enhancing relationships, fostering artistic creativity, and being in flow in your life and endeavors.
Dodecahedron (Universe/Spirit): Representing the Universe (or ether), you can use the dodecahedron for manifesting spiritual growth and connection to Universal Wisdom. It can aid in deeper meditation, enhancing psychic abilities, and understanding life’s purpose.
For all of their elegant simplicity, the platonic solids stand as a testament to a vast universal interconnectedness of which we are a part. They serve as a beautiful reminder of our place within this intricate and harmonious existence, bridging the physical, spiritual, and intellectual dimensions of our world.
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