Historically, various cultures have viewed geometry with an almost religious significance, believing it could decode universal truths. It played a key role in these ancient societies, and studying it held a near-mystical quality. 

The practice of assigning symbolic or religious meaning to shapes still happens to a significantly lesser degree. While it’s viewed differently today, there are occasional flashbacks of our geometric past in things like the resurgence of the geodesic domes in meditative practice.

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Table of Contents

In this article, we’ll cover:

• The Basics of Sacred Geometry
• How Plato Viewed The Platonic Solids
• The Flower of Life Symbol and Related Shapes
• Introduction to Fractals as the Shape of Nature
• Geodesic Domes and Their Potential Benefits

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What Is Sacred Geometry?

Sacred geometry views certain symbols and shapes as having religious or symbolic meaning. Until around the Middle Ages, nearly every society with numbers was also studying shapes and the relationship the two shared. 

Math was tied to philosophy and spirituality, particularly through its implications for astronomy. Geometry could map the patterns of the sky, giving astronomers the ability to predict the future. 

Plato, the ancient Greek philosopher, believed geometry was an integral part of his worldview. One modern-day mathematician explains Plato’s philosophy this way: “The nature of things and the structure of the universe lay in the study of music, astronomy, geometry, and numbers [1].” 

Similar shapes, patterns, and ratios commonly appear in nature and throughout the universe. Recognizing these can change the way we view the world around us, and it certainly did for them.

Geometry would maintain this philosophical and semi-religious role until the scientific revolution of the 16th and 17th centuries. Though geometry isn’t typically thought of the same way today, the echoes of this past ring through to the present.

Some of the images from antiquity still appear today, though often without their original meaning. 

What Are the Platonic Solids?

2,300 years ago, Plato postulated that everything in the physical universe consisted of one of five three-dimensional shapes [2]. The perfectly symmetrical solids are made of either equilateral triangles, squares, or pentagons joined together.

A breakdown of the shapes — also found in 4, 6, 8, 12, and 20-sided dice (correlating to their sides) — is below:

Each of these follows a strict set of rules that make them perfectly symmetrical. Every face, line, angle, and connection has the same measurement and placement. 

Plato argued that these shapes were the building blocks for all matter in the physical world. 

Nearly two-and-a-half centuries later, nobody has found another solid outside of Plato’s five to follow these rules. Plato wasn’t the first to discover these shapes or ponder their importance, however.

Archaeologists disagree, but many believe a set of stones carved over two thousand years before Plato represents at least four of them [3]. Given the other archaeological evidence, Plato is likely not the first to ascribe significance to them. 

Here’s more information on the relevance and symbolism of each:

The Tetrahedron, A Fundamental Building Block of Fire

Using the fewest faces to form a complete shape, the tetrahedron is the simplest Platonic solid. It’s also the sharpest and least rounded, with each of its 4 points on a triangular base. 

Plato stated that this one was the building block for fire, representing the element’s agility with its simplicity [4]. The sharp angles could help break things apart, representing the destructive and energetic power of fire.

The Cube, A Fundamental Building Block of the Earth

Plato (who believed everything revolved around the Earth) wrote the following in Timaeus:

Since Earth is the most immobile of the four types and it is the most malleable of bodies, so it is especially necessary that this be the sort that has the most stable bases

The bulkiness of a cube makes it a perfect candidate for Earth, representing stability and strength. Other shapes with rounded or triangular bases were too easy to move, but a box stands firm and provides shelter.

The Octahedron, A Fundamental Building Block of Air

The Octahedron isn’t as smooth as water (the icosahedron, below) but is smoother and less mobile than fire (the tetrahedron). While air flows like water, the fluidity of water’s movement makes it seem “smoother” than air at a fundamental level to Plato.

While air is weightless, it’s still strong and can get through or around most obstacles. Using the more stable shapes of square-based pyramids makes this solid less rigid and lighter than other shapes, except for fire (tetrahedron). 

This last point helps make Plato’s argument since fire rises in the air.

The Icosahedron, A Fundamental Building Block of Water

Water is given the largest, third-sharpest solid, representing how it can take up the space of any container and cut through canyons over time. Its many faces give it a smooth appearance that Plato believed was representative of flowing water.

Additionally, this solid breaks up easily into others, fits within many other shapes, and can easily attach to others. This versatility makes it an ideal candidate for water’s permeability.

The Dodecahedron, A Fundamental Building Block of Aether

Aether — modernized as “ether” — is a mysterious force behind the creation of the universe and the powers of a creator. Plato said it was “the purest” form of air and that “the divinity” used the dodecahedron to establish order within the universe:

Thus therefore, the divinity placing water and air in the middle of fire and earth, and rendering them as much as possible analogous to each other, so that what fire is to air, that air might be to water, and what air is to water, that water might be to earth, he bound together and constituted the heaven, visible and tangible (emphasis mine)

In this passage from Timaeus, Plato illustrates his view of “aether” as an essential component of the heavens. It was the building block for a world (or worlds) above ours, reserved for deities.

What the Flower of Life Represents

The Flower of Life consists of 19 overlapping circles representing unity, interconnectivity, and the life cycle. The oldest instance of this pattern dates back to at least the 7th–8th century BCE [5], but its peak usage was the 1st–2nd century CE. 

Given the age of this symbol, it’s impossible to know its age or the initial circumstances of its creation, but it appears on several artifacts. Some scientists claim it appears in artifacts from 2,500 BCE [6].

Independent researcher, Marko Tapio Manninen, summarizes it this way in his book:

We would probably just say that we cannot know what was meant with the symbol, or we cannot be sure where and why it was made, since none of it is nor written or told on any ancient sources. But would we know even if someone told?

Several symbols have come from this, and three other sacred shapes are involved in its creation. These are:

1. The Sacred Circle
2. Vesica Piscis
3. The Seed of Life

Here’s more information on each:

Why Was The Circle Sacred

The Flower of Life is made of circles, so the first step would be a single one, which is symbolic itself. Circles represent infinity and completeness, like the current meaning of wedding bands.

A circle is considered special since it has no beginning or end and is perfectly symmetrical with a single, infinite line.

The Christian halo may have a relation to this, especially in older iconography, where the halo is often a solid circle. Similarly, the Yin and Yang symbol (which is in The Flower of Life) may represent the duality of forces throughout the eternal universe.

The Meaning of Vesica Piscis

If you took your compass to the top of the first circle and created another one centered on its edge, you’d have the Vesica Piscis. The shape of a Venn diagram, this symbol shows two forces merging to form an eye. 

Some interpret this as heaven and Earth (or a divine masculine and feminine force) meeting to form our observable universe. 

The two circles coming together to form a third space also represent fertility, interconnectedness, and dual forces within and outside the observable universe.

When Christianity was still an illegal religion, they used a fish to covertly mark churches. The word for fish was a code with each letter meaning “Jesus Christ, Son of God, Savior,” but the image may have come from the Vesica Piscis.

The Seed of Life Meaning

By adding six circles around the initial one’s border, the Seed of Life symbol appears. It represents a variety of things, often related to the creation of the universe or the circle of life. 

In Christian thought, it is the creation of the universe, linking the seven circles to the seven days of creation. In Buddhism, they may also represent the seven steps to enlightenment and humanity’s ability to achieve it.

The interweaving of the circles showcases the interconnectivity of creation and the elements of life.

Symbols Related To The Flower of Life

Several other images throughout the centuries have come from the Flower of Life in one way or another, including:

• Tree of Life (Kabbalah) — This popular symbol in Jewish mysticism, representing creation, life, and the afterlife, fits perfectly within circles in the Flower of Life
• The Fruit of Life — A 13-circle pattern found within the Flower of Life, the Fruit of Life symbol represents unity and the interconnectedness of creation
• Metatron’s Cube — Several lines connecting 13 circles from the Fruit of Life yield a complex shape containing all five Platonic solids (technically, three of them and two “look-alikes” [7])
• Merkaba — The six-sided star used in Judaism forms when connecting some of the circles from Metatron’s Cube 
• Yin and Yang — This symbol, representing dual yet complementary forces, exists within the Flower of Life image

These are just a few of the symbols related to the Flower of Life, with many others fitting within it and Metatron’s Cube.

What are Fractals?

Fractals are complex geometric shapes with never-ending, ever-repeating patterns. Due to this, anywhere you zoom in on a fractal, the same image appears as each part of the image also displays the whole. 

The Koch Snowflake, based on the work of Swedish mathematician Niels Fabian Helge von Koch, provides an example [8]:

1. Begin with an equilateral triangle
2. Remove the middle of each side and replace it with another triangle
3. Repeat the process indefinitely

Eventually, you’ll wind up with a snowflake with an infinitely repeating pattern. It would be just one line, but that line would be infinitely long despite the shape not appearing to grow in size.

Much of the history of fractals owes its popularity to the introduction of computers. Before the introduction of computers, fractals were considered largely theoretical, though they had been discussed in one form or another for centuries.

The Shape of Nature as a Fractal

In 1977, the Polish-French mathematician Benoit Mandelbrot argued that nature was a fractal shape in “Fractals: Form, Chance and Dimension.” 

He opens with:

Many important spatial patterns of nature are either irregular or fragmented to such an extreme degree that… classic geometry…is hardly of any help in describing their form. The coastline of a typical oceanic island, to take an example, is neither straight nor circular, nor elliptic, and no other classical curve can serve without undue artificiality… [9]

A few years later, Loren Carpenter, a designer for Boeing, stumbled upon this book, and it opened his eyes to a new way of thinking. Carpenter created computer-generated imagery for the aircraft company and wanted to create a realistic-looking landscape, unheard of in 1979.

After the book, Carpenter reasoned he could generate more realistic landscapes on his computer by utilizing fractals.

He began with some rough triangles and began breaking them up over and over. After several iterations of this, he created the most realistic generation of mountains the world had ever seen. 

The video he created for a conference he heard would have Hollywood executives at is below:

https://vimeo.com/5810737 

(“Vol Libre,” by Loren Carpenter, demonstrating the use of fractals to create computer-generated landscapes.)

He was immediately hired by Lucas Films, as the book, “Droidmaker: George Lucas and the Digital Revolution” describes:

The audience erupted. The entire hall was on their feet and hollering. They wanted to see it again. “There had never been anything like it,” recalled Ed Catmull, [VP of Lucas Films]. Loren was beaming. 

Two years later, Carpenter would use these same images to create a realistic-looking planet for Star Trek 2: The Wrath of Khan.”

https://youtu.be/Tq_sSxDE32c?si=IMTVKxw1O3ioW6E4 

What Are Geodesic Domes?

Geodesic domes are thin, spherical structures that utilize principles of geometry and physics to create sturdy, inexpensive, and impressive shelters. They take a fractal-like approach, starting with a Platonic solid (the icosahedron) and breaking it into smaller portions.

They were invented in 1913 by Dr. Walther Bauersfeld, popularized first by R. Buckminster Fuller, and are now experiencing a resurgence in popularity. There are several benefits to geodesic homes, including their ease of construction and use of minimal materials.

The Invention of Geodesic Domes

Dr. Walther Bauersfeld first designed the structure in 1913 to create the first planetarium [10].

Until this point, “Star Theaters” consisted of small, spherical rooms with rotating ceilings, mimicking the movements of the night sky while fixed projectors shone on the outside. The Deutsches Museum in Munich tasked Bauersfeld with improving this for a large crowd.

Bauersfeld first created a mobile stand with 32 projectors to illuminate the room from within, removing the need for rotating ceilings. 

Next, he needed a flat surface for each of the 32 projectors, so Bauersfeld started with the Platonic solid with the most faces — the icosahedron. He broke it up and adjusted it slightly to add the additional 12 faces needed for his fractal-like dome.

The spherical shape distributes its weight evenly, creating a large, open area without supporting beams or walls. A metal frame with a thin layer of concrete sprayed along the outside made up the structure.

Bauersfeld patented the structure in 1925 [11], describing it as:

A spatial network of iron bars which bears its own weight as well as part of the total weight of the concrete. A lightweight form is placed behind the network while spraying the network with concrete, thereby implanting the network in concrete and giving the shell its full strength.

The wall only needed to be proportionally as thick as an eggshell to ensure structural integrity, thanks to the spherical shape.

While Bauersfeld made a few of these planetariums, they never achieved broad recognition. Just one year after his invention, Germany was plunged into World War 1, and he could no longer find support to continue his project.

R. Buckminster Fuller’s Geodesic Vision

R. Buckminster Fuller was an architect, philosopher, inventor, writer, and more. The undercurrent for much of his work was a love for geometry and its implications on innovative housing solutions.

In 1947, Fuller was recovering from the failure of his company, Fuller Houses, Inc., and had very little money [12]. His design for the “Dymaxion” home — named to signify the maximization of minimization — was a national hit, but only two were built before the company liquidated.

He began teaching at Black Mountain College, an unaccredited university associated with several famous and influential people. Over two Summers, Fuller and his students attempted various versions of the geodesic dome before finally achieving the current form.

In the end, his success came down to a principle of “Tensegrity” — improving structural integrity with tension [13]. This combination of equally dispersed tension along with sturdy, geometric structures produced a highly efficient home using minimal materials.

His patent, filed in 1951, does not mention the 1925 patent by Bauersfeld or his planetariums. It’s unclear if he knew about them or not, but geodesic domes seemed to have serious implications for housing, military use, and more. 

One 2016 study on monolithic and geodesic homes for housing scenarios found:

The triangular spherical configuration of geodesic domes give it unique structural capabilities unmatched by other structural systems. Steel geodesic domes have been wind tunnel tested to withstand up to 200 mph winds. As long as the height and span correspond, a geodesic dome can be of any size [14].

Like his Dymaxion home, the geodesic home wouldn’t be a success for Fuller. He only sold a couple of them as mobile bases for the military —  a far cry from his vision.

Benefits of Geodesic Domes

The spherical structure and symmetrical harmony of geodesic domes provide several unique benefits. Advantages range from structural to mental and potentially even spiritual. 

Here are some of the reasons a geodesic dome is superior:

1. Structural Integrity — The symmetrical shape and domed structure distribute weight evenly throughout, making it resistant to wind, earthquakes, and more
2. Embracing Openness — There’s no need for a supporting wall or dividers within a geodesic dome (at any size), making open environments easier to cultivate
3. Closer to Nature — Geodesic domes use fewer materials than most structures and often include windows and other openings, making it easier to feel in touch with the surrounding world
4. Harmonious Structure — Sitting within the symmetrical presence of a geodesic dome can feel almost mystical on its own

Geodesic domes are uniquely capable of both aiding in meditation and providing cheap, efficient housing capable of withstanding extreme conditions.

Where To Find Geodesic Domes in Tennessee

Nature retreat centers like Bask Retreat Center in Tennessee offer geodesic homes as domiciles, meditation rooms, and meeting places. They’re fantastic for reconnecting with nature while meditating, doing yoga, or simply reflecting.

Pairing this with the beautiful backdrop of Tennessee’s biodiversity, settling into relaxation and comfort will feel easier than ever. Some people claim the benefit is spiritual or even magical, but the true reason they’re special isn’t mystical; it's geometric. 

If you want to visit a geodesic dome as part of a nature retreat, try booking one with Bask Retreat Center to see for yourself.

Conclusion: The Shape of Life, Matter, and Nature

Geometry was once a sacred practice, and many of the shapes we still hold on to (like the Flower of Life) are rooted in ancient beliefs. Understanding the world around us and how it interacts with itself through geometry can help unlock a better comprehension of life.

Geodesic domes utilize harmonious geometry for a more impactful meditation, retreat, or other form of self-care. While R. Buckminster Fuller’s vision of affordable housing never came to fruition, it’s making a resurgence thanks to meditation and retreat centers.

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References

1. Gorini, C. A. (2000). Geometry at Work. Cambridge University Press.

2. Plato. (2001). Plato: Timaeus (P. Kalkavage, Trans.). Focus.

3. Lloyd, D. R. (2012). How old are the Platonic Solids? BSHM Bulletin: Journal of the British Society for the History of Mathematics, 27(3), 131–140. https://doi.org/10.1080/17498430.2012.670845

4. Tarrant, H. (2011), Proclus: Commentary on Plato’s Timaeus: Tarrant, Harold: Amazon.com: Books.

5. Perrot, G., Chipiez, C., & Armstrong, W. S.. (2012). A History of Art in Chaldæa & Assyria; Volume 1. Wentworth Press.

6. Manninen, M. T. (2016), Creative power of the Flower of Life,  Open-source.

7. Mitrovic, I., Krasic, S., Tomic, J., & Kocic, N. (2024). Construction of Three-Dimensional Model of Platonic Solids Utilizing Metatron’s Cube. Journal of Industrial Design and Engineering Graphics, 19(1), Article 1. https://www.researchgate.net/publication/383422736_CONSTRUCTION_OF_THREE-DIMENSIONAL_MODEL_OF_PLATONIC_SOLIDS_UTILIZING_METATRON'S_CUBE

8. Weisstein, E. W. (n.d.). Koch Snowflake. Wolfram MathWorld. Retrieved May 9, 2025, from https://mathworld.wolfram.com/KochSnowflake.html

9. Mandelbrot, B. B. (1977). Fractals: Form, Chance and Dimension (2nd edition). W. H. Freeman and Co.

10. Fernández-Serrano, M. P., & López, J. C. (2017). Projecting Stars, Triangles and Concrete: The Early History of Geodesics Domes, from Walter Bauersfeld to Richard Buckminster Fuller. Architectura, 47(1–2), 92–114. https://doi.org/10.1515/ATC-2017-0006

11. Rothman, T. (2014). Science a la Mode: Physical Fashions and Fictions. Princeton University Press.

12. Pawley, M., & Fuller, R. B. (1990). Buckminster Fuller. Parkwest Pubns.

13. Fuller, R. B. (2019). Everything I Know. Buckminster Fuller Institute.

14. Abraham, R., & Chandran, K. (2016_ Study of Dome structures with specific Focus on Monolithic and Geodesic Domes for Housing. International Journal of Emerging Technology and Advanced Engineering, 6, issue 8. https://www.researchgate.net/publication/349138511_Study_of_Dome_structures_with_specific_Focus_on_Monolithic_and_Geodesic_Domes_for_Housing