“Geometry is a science explained by Pythagoras and demonstrated by him. It is the science of God and its formulas are illustrative of the fact of the very energy of life that can be focused in the angle, in the pyramid, in the octagon, in the cell structure that is also geometric. Form itself designed by God is a protection for the eternal flame. Even the form you wear has a design of the star-fire body intended to be, geometrically speaking, the ultimate protection for the soul. The geometry of the chakras and the beauty of the unfolding of the flower becomes a model of contemplation that ought to be considered when designing the physical temple …. Thus, beauty and mathematics, proportion and the golden ratio serve to enhance the message of the Word itself.”
Sacred geometry is based upon the idea that everything in nature, and therefore within ourselves, from the smallest configuration of subatomic particles to the blazing hearts of stars and the majestic rotation of galaxies, is based on five basic solids and a handful of mathematical concepts which are instantly recognizable by most people for their results if not by name. While these ideas trace back to Ancient Greece and in fact are based upon observations by philosophers such as Plato, traditional academia largely neglected or outright scoffed at the idea of sacred geometry until the early 1980s.
A researcher at the University of Chicago demonstrated conclusively that the basic structure of every element in the Periodic Table, the building blocks of our physical reality, all conformed to the five Platonic Solids. In chemistry, physics, art, engineering and other academic disciplines, the concepts of sacred geometry are being routinely rediscovered and incorporated into the accepted knowledge and “conventional wisdom” of these topics. Because of advances in the various sciences, concepts which were familiar to the ancient Greeks and other advanced civilizations of the time are only now being rediscovered. Let us consider the precepts and ideas of sacred geometry further, to see how sacred geometry affects our world and our lives on a daily basis.
The Numbers Behind Sacred Geometry
Sacred geometry revolves around three basic numbers: the square roots of 2 and 3 and the so-called “Golden Ratio.” These numbers are readily identifiable to mathematicians, artists and architects, but a closer look suggests that everything we see around us is directly linked to these basic numbers.
The square root of 2, or ~1.414, is also the ratio of the hypotenuse of a right triangle to the lines forming the other two sides at 90 degrees. Mathematically this can be used to solve basic trigonometry problems and expands into topological considerations. For our purposes, this number also signifies the concept of two pieces, the square root of 2 times itself, creating something greater than the sum of its parts. While this is an irrational number, as 2 does not form a perfect square, the result is quite tangible and readily visible in a number of natural and manmade
The square root of 3, or ~1.732, can be best expressed by considering a Venn diagram where the centers of both circles touch each other. This figure is also known as the Vesica Piscus, or “fish’s bladder,” because of its shape. This shape suggests common ground or looking into someone else’s soul, as well as symbolizing tripartite deities or concepts such as Maiden, Mother, Crone or Father, Son, Holy Spirit. In the latter meaning, or in some cases possibly as a subtle allusion to the former, this symbol often appears in overt and covert forms in the works of many Renaissance artists.
The “Golden Ratio,” or ~1.618 or phi, pronounced “fee,” is the most obvious and self-apparent to the layperson. This number is a central basis of visual arts, architecture and sculpture. In addition, you can see the Golden Ratio at work in the spiraling chambers of a nautilus snail, the proportions of the Parthenon in Athens, Greece, the form of the Venus de Milo and the construction of the “ideal” human face and body of both genders. This can also be seen in the shape, proportions and ratio of the individual portions of a “perfect” pentagram.
The Fibonacci Sequence, or 1,1,2,3,5,8,13,21,34… is another familiar example of the Golden Ratio given a slightly more “user-friendly” form. These numbers each lead to the next following the Golden Ratio. You can see Fibonacci distributions in the way the individual seeds of a pine cone are arranged. Additionally, a Fibonacci progression often exists in self-generating systems such as rabbit populations, spirals and the underlying shape of geometric fractal patterns.
The Forms and Shapes of Sacred Geometry
The most basic form in sacred geometry, as with the type of geometry you probably studied in high school or college, is the point. This is a one-dimensional location which is isolated in space and therefore does not practically exist except as a beginning or end of a journey. Two points are connected by a line. Multiple points form a plane. Multiple planes form a solid. The exceptions to this rule are the circle, which has no practical beginning or end, and the sphere, which is the solid iteration of a circle. Beyond these are the Mobius strip, commonly known to the layperson as the infinity symbol, which reduces a two-sided surface to a single-sided surface. You can actually make one of these at home by tearing off a strip of paper, giving it a half-twist and joining the ends. One step further in complexity is the torus, which is essentially a doughnut shape. If you play three-dimensional video games, you have likely encountered this form without realizing it, as most video games are programmed using a torus as the playing field. This is why the horizon may appear to curve upward at times during gameplay, especially during times of high lag or onscreen activity.
Outside of the shapes listed above, sacred geometry takes into account five Platonic Solids, which also serve as representations of the five primal elements the ancient Greeks acknowledged. These regular solids, meaning all the sides are identical in angle and shape, are:
- Tetrahedron: A four-sided solid figure, expressed as a three-sided pyramid. This symbolizes fire. Also known as a “dual” with the octahedron because combining two of these figures creates an octahedron if the axes are aligned properly.
- Hexahedron: A six-sided solid figure, also known as a cube. This symbolizes earth.
- Octohedron: An eight-sided solid figure. This symbolizes air. Also known as a “dual” of the tetrahedron.
- Dodecahedron: A twelve-sided solid figure. This symbolizes “aether” or spirit.
- Icosahedron: A twenty-sided solid figure. This symbolizes water.
In addition to the Platonic Solids, there are also thirteen Archimedean Solids, so named for the Greek philosopher and mathematician Archimedes. These are also known as “tessellations,” in which multiple shapes make up the form. Archimedean Solids are considered “transitional solids,” demonstrating movement, change and alteration between Platonic Solid forms. For the sake of convenience, we will list the entire evolution from the tetrahedron to the icosahedron, showing how the Archimedean Solids fit in their intermediate states between Platonic poles. This illustrates not only the evolution of the elements, but the ascent from the physical world to the spiritual heights represented by the icosahedron.
- Truncated Tetrahedron
- Truncated Cube
- Snub Cube
- (Rhombi) Truncated Cuboctohedron
- (Dymaxion) Cuboctohedron
- (Mecon) Truncated Cuboctohedron
- Truncated Dodecahedron
- Snub Dodecahedron
- (Rhombi) Truncated Icosidodecahedron
- Truncated Icosahedron
You may notice that the five Platonic Solids and thirteen Archimedean Solids are both numbers that occur within the Fibonacci Sequence. Additionally, with the number 12, 5 and 13 express the sides of a perfect right triangle, whose hypotenuse is expressed by the square root of 2 as above.
The highest degree of complexity with regards to sacred geometry involves stellations. These three-dimensional starburst shapes are produced by putting Platonic and Archimedean forms together. The ramifications of these shapes can become quite complex, but may also serve as guideposts to aid your spiritual growth and evolution, as we will see below.
Sacred Geometry Is All Around You
The forms of sacred geometry are expressed in everything, at every level of physical existence. You can even find evidence of sacred geometry in your own DNA, because of the double-helix formation of it. Like any other spiral structure, DNA follows the rules of the Fibonacci Sequence, the proportions described above and sacred geometry. Thus it quite literally is present in your own genes.
In nature, the forms of sacred geometry exist in mineralogical deposits, typically in crystalline forms but sometimes elsewhere. For this reason certain minerals are often considered to be attuned to the elements represented by the forms of sacred geometry. These minerals may be made into jewelry, strung on a necklace or simply carried on your person. Likewise, plants or natural objects that follow these forms may be employed as emblems of concepts in sacred geometry. How these objects might be used and what their greater implications will be considered below.
The Metaphysical Uses of Sacred Geometry
Sacred geometry can be employed as a tool for understanding yourself and the people and things around you. For example, if you are very passionate but often lose your ability to think clearly when your emotions are aroused, you might wish to consider that you are closer to the fire figure than the air figure, which is associated with the mind. If you are deeply spiritual but often lose track of more terrestrial concerns such as when the bills are due or the fact your spouse, partner or significant other misses you, you may wish to simplify and reduce the number of “sides” in the form that represents your position in the evolutionary chain from the physical to the spiritual and cerebral realms. When studying for an important test or examination where you need to retain a great deal of information, you might try raising yourself to the realm of air to stimulate your higher cognitive and recall faculties.
Similarly, you can use sacred geometry as a basis for familiarizing yourself with the psychology and needs of other people around you. If you would like your significant other to be more amorous, you might want to consider ways to activate the fire in their being. If you want your friend to be more understanding about your spiritual beliefs, you may examine what “rung” of the geometric “ladder” your friend is on versus your own as a basis for determining where the disconnect falls between the two of you. This can form a foundation for establishing common ground or attempt to help the other person resolve an internal or external conflict outside his or herself.
With study and practice, and a great deal of honest soul-searching, sacred geometry can add immeasurably to your personal understanding of yourself and your place in the world around you. If you are willing to put in the effort, you may also be able to give deeper and more detailed analysis, as well as suggest more nuanced and balanced possible solutions to problems. Under no circumstances should you ever use sacred geometry to actively try to affect someone else without their informed consent. Without such consent, your best bet is to try to understand the other person and see if you can work within yourself to meet them on their level. However, as a rubric for understanding someone else or yourself, or when you are sufficiently familiar with the workings and concepts of the practice to employ it effectively on your own, you will find sacred geometry to be a very powerful and useful tool.