** In2Infinity **

Welcome to our Ultimate Guide to Sacred Geometry. Discover the wonders that this intriguing art form can unveil. From mystical and spiritual realms, to new wave scientific thinking, Sacred Geometry expresses a fascinating world view that inspires and delights the mind.

✔ Sacred Geometry can be practice by anyone of any age who can hold a drawing compass

✔ All constructions are derived from the initial compass opening of ONE.

✔ Sacred Geometry is found through human history inspiring great thinkers like Da Vinci.

✔ The practice of Sacred Geometry explores a wide range of disciplines from the scientific to the spiritual

## Introduction

Sacred Geometry is defined as drawing without measurement. It involves the tools of drawing compass and ruler, but unlike traditional geometry, all shapes and dimensions are interrelated and arise from a pattern of overlapping circles. The ‘sacredness’ of geometry comes from the intuitive side, containing meaning – the basis of sacred geometry. Here are a few key-points:

It is related to spiritual symbolism and architecture.

It explains that all of nature’s patterns can be related back to shape.

It suggests that the Universe is designed by a blueprint that expresses itself on all scales, from the atom to the galaxy.

In this Ultimate Guide to Sacred geometry, you will find an in-depth overview of all there is to know about the most intriguing patterns of the history of humankind!

##### Content:

### What is Sacred Geometry?

Tools

Rules

Meaning

Benefits### History

Architecture

Sacred Geometry in the Church, Mosque or Temple

Art & Design

Alchemy Symbols

Sacred Geometry Logo

Sacred Geometry Tattoo### Symbols of Religions

Islam

Christianity

Judaism

Buddhismus

Hinduism

Taoism### Overlapping Circles

The Beginning

The Dot

The Line

The Circle

Vesica Piscis

2D

Trinity

Trion Re

Seed of Life

Egg of Life

Flower of Life

Fruit of Life

Metatron’s Cube

3D

Sphere

Platonic Solids

Archimedean Solids

4D

Torus

Hypercube

5D & Higher dimensions

Double Torus

5D Merkaba### Mandala

Design

Mandala Flower

Meaning

Mandala to colour

Mandala Tapestry### Patterns in Nature

Fibonacci Spiral

Golden Ration

Silver Mean

Fractals### Science

Cymatics

Geometry of Light

Atomic Geometry

Molecular Geometry

Solar Geometry

## What is Sacred Geometry?

The word itself consists out of two parts: Sacred and Geometry. This means that it is rooted in traditional geometry which we can trace back to Ancient Greece, Ancient Egypt or Ancient India. The crucial reason why Sacred Geometry is different to the Geometry we learn in school is that it is based on a very distinct pattern that arises from just overlapping circles. A geometric puzzle so to speak, that transforms from one form into another and ultimately creates all shapes that exist. It is a worldview of pattern recognition, an architecture of space and time, which has arisen out of the study of natural forms. It is considered sacred as it is believed that each shape holds divine rules, mysteries, and the grander design of the cosmos, which can be understood through geometry.

## The benefits of learning Sacred Geometry

When we draw these sacred designs, it works like a key in a lock to open up new horizons within our brain. Just the fact that geometry works on us visually, our brain already gets rewired and at the same time, the knowledge each form encodes helps us to unfold new concepts about the Universe. Then, we can contemplate on these ideas having a geometric structures in our mind than gives as a grounded idea of spiritual concepts and at the same time, simplifies science. That is, we get smarter opening up new thought processes to enhance the way we think, our problem solving skills, our moral compass. Being more aligned with universal laws, it reflects in our efficiency to come up with new ideas and solutions for almost any field of society, such as architecture, technology, education and agriculture. Many healers and energy workers work with sacred geometry for healing. There are many meditations that use geometric visualisations to energise, heal and work with the field around us to enhance our wellbeing. Ultimately, it is the structure we live in and we’re made out of, so by learning about it we become more in harmony with life.

## The Tools

The basic tools you need for Sacred Geometry practise is a standard drawing compass and straightedge. With the drawing compass you can draw circles, with the rulers, lines. In Ancient Greece they used a rope rotating around a fixed point to draw circles, something that works well for large designs. Amazingly, these tools are also representative of the two forces inherent within sacred geometric philosophy. The circle represents the feminine aspect, that is all encompassing, and is also expressed in 3D as a Sphere. The ruler is the straight and directive energy, the masculine tendency of life, that exists inside the circle or sphere. This is a geometric fact, as a circle will encompass any regular shape (made from lines), no matter how many sides it has. The same can be said of any of the 5 Platonic Solids that nest perfectly inside a sphere. Just from a circle and a line, everything else can be created.

Here is an overview of what you need:

Drawing compass

Ruler

Pencils

Paper (A4 is fine, A3 is better)

Colours

## The Rules of Sacred Geometry

Each geometric design holds information in a specific order that can be reproduced every-time we draw it. To be able to do so, we need to follow these principles of Sacred Geometry:

All shapes and patterns are created without measuring.

We always start with a circle. The first compass opening is defined as a radius of one.

All other ratios derive from this first value and are always constant.

The second step is always another circle that can be created anywhere from the circumference of the first. Without changing the radius, this will form two equally overlapping circles (Vesica Piscis).

From here, the pattern follows a simple blueprint, where new circles or lines can only be created from the intersection points (nodes). There is no randomness.

We can only connect nodes to form shapes, when that node is surrounded by a circle. This is because the dot and the circle are inverse to each other. Whenever there is a dot, there has to be a circle surrounding in, just like the nucleus is surrounded by the electron cloud in the atom.

A lot of people draw Sacred Geometry without adhering to these rules and do not see the pattern unfolding in a specific way. Even though from a design point of view, you can do it in other ways, we do suggest for you to stick to these rules, as these reveal to us how nature operates.

## History

Sacred Geometry is rooted in the study of geometry and goes back as far as humanity’s understanding of the first circle. In modern times, Sacred Geometry was coined by Robert Lawlor in relation to the significance of certain geometrical forms and principles that explain the natural world from a metaphysical point of view. The term was further popularised by Drunvalo Melchizedek (an esoteric practitioner) and a plethora of other personalities from all walks of life such as Artists, Designers, Architects, Mathematicians, Scientists and Spiritual practitioners among others.

Today, the term has been widely established in the New Age movement to describe a specific geometric pattern that shows the interconnectedness of all things. What we have found out is that there is a lot more science to it than many people acknowledge and deep philosophical concepts hidden in pretty patterns. The more you dive into the study of Sacred Geometry, the more it becomes clear that there is a riddle in front of our eyes just waiting to be solved.

## Antiquity

In many ancient sites to modern day buildings, we find the idea of proportion and ratio. Often we see certain designs carved into stonework as well as incorporated in the architecture. This appears in almost all places of worship and various sacred sites such as temples, mosques and churches, which is significant as it demonstrates a universal spiritual bond that is found in the archetypes of sacred forms. This is also one of the reasons why it is called Sacred Geometry.

## Alchemy

Alchemy is an ancient branch of natural philosophy, which goes back to different cultures around from China, India to Ancient Egypt. One of the aims of alchemy was the creation of gold from metals, the philosopher’s stone. Much of the work was related to magick, mythology and spirit to reach immortality and was kept secret using cyphers and symbolism. Some of the Sacred Geometry Alchemy Symbols are the four elements, symbols for some of the elements such as Zinc, Copper, Silver, Sulfur and Gold.

## Architecture

Geometry goes back to the architecture of Ancient Greece, Ancient Egypt, and Ancient India. One of the most famous example is the great pyramid of Giza, which is a scaled representation of the earth, the moon, and our own human bodies. Yet, the oldest structures that have geometric proportion are found in the stone circles from the Neolithic era. These Stone circles are made from very large stones called Megaliths, which are prehistoric structures (especially in western Europe). The best known example of megalithic structure with special geometric connotations is the Stonehenge in Britain.

## Churches, Mosques & Temples

Sacred Geometry is found in many architecture concerned with religious practise around the world. Also termed Sacral architecture, sacred architecture or religious architecture, the design and construction of churches, mosques, temples, stupas, and synagogues are amongst the most impressive buildings created by humanity. Not only the fundament of these structures are often based on the principles of Sacred Geometry, also the interior uses a lot of iconography, signs, and symbols. What’s interesting about these majestic buildings is, it affects the eye as well as our well-being. Often, we feel very calm and meditative inside of a church or temple. The most simple but striking example of geometric symbolism definitely includes the cube at the center of Islam’s most important mosque, the Masjid al-Haram in Mecca, Saudi Arabia.

## Art & Design

Sacred Geometry Art has always something very mysterious about it. Is it the pure beauty it contains or their spiritual aspect, from the artwork in churches and cathedrals to the modern day, you always get inspired by it. Leonardo DaVinci, whom the world knows as a great painter, architect, inventor and one of history’s greatest enigmas was also a key figure in the advancement of the art and study of sacred geometry. DaVinci studied geometry (and the sacred geometry principles therein) under Luca Paciolli. He also illustrated the diagrams and sketches in the famous book written by Paciolli titled ‘De Divina Proportione’ which literally means ‘The Divine Proportion’ in Italian. Divine proportion (or otherwise known as the golden ratio) is one of the most celebrated geometric proportions in sacred geometry (and all of mathematics indeed). Leonardo DaVinci is also known to have studied human anatomy through dissection of corpses and illustrated the “Vitruvian Man” which was again based upon the divine proportion and other important relationships found in the human body as stated by the Roman architect Vitruvius (1st century B.C.). Interestingly, this image does not only relate to the anatomy of the body, but also the Moon and Earth, the Sandreckoner Diagram, squaring of the circle, Stonehenge and the mysteries of the Great Pyramids of Giza. In his sketch book, we find the Seed of Life pattern and the Flower of Life, which indicates, he was indeed someone who was well educated in the universal laws. It is therefore not surprising that he was much more than an artist, but a polymath, someone who was well-educated in many field. Could this be because of sacred geometry?

From the Renaissance period and Leonardo DaVinci, today, Sacred Geometry is apparent in many designs. In the spiritual community, we see Sacred Geometry symbols on printed on T-shirts, blankets, jewellery, on mugs, posters, yoga matts und much more. One thing is for sure, the more we align art and design to Sacred Geometry, the more we resonate with that piece, the more we feel it is beautiful.

## Logos

To use Sacred Geometry in Logos is becoming a trend, yet it is not a new thing. Many corporation use sacred geometry for years already. Just have a look at the logos of Mercedes, Gucci, Apple, Mastercard or Twitter, they are all based on the principles of Sacred Geometry! Why this is so can only be answered by getting a deeper understanding of these symbols.

## Tattoos

Who doesn’t want a Sacred Geometry Tattoo?

It’s become quite cool to have symbols such as the Flower of Life or the Tree of Life tattooed on our skin. Often people of a more awakened mind have started to look for deeper meaning behind beauty, so we see it almost on every spiritual gathering, it even was the theme of 2018’s ‘Boom’ festival in Portugal. So, it’s no surprise that Sacred Geometry has been becoming a trend for tattoos. What many do not know, is that multi-layered meaning behind each symbols beyond their apparent beauty.

## Religious Symbols

Just as in religious architecture, also in religious symbolism, we find Sacred Geometry. These ancient symbols are engrained with the respective cultures, which are related to great meaning and connection to the divine. In this section, we’ll explore the most common symbols and what they represent from Islam, Christianity, Judaism to Hinduism, Buddhism, and Taoism to name a few.

## Islamic Art

Judaism, Christianity and Islam are all rooted back to the God of Abraham. That’s why they are also know as the Abrahamic religions. In contrast to other religions, in Islamic we do not find any figurative images of god, instead there is Sacred Geometry everywhere! Much of Islamic art represents the divine reality through geometric patterns. Many tapestries are based on the grid of the Flower of life tapestry, with a recurring motif being the 8-pointed star, the Octagon, two squares rotated at 45°. More complexity is being created with repeated squares, circles and pentagons up to 6- to 13-, 14- and 16-pointed stars, which may overlap to form intricate and complex patterns. All of these be constructed on grids that require only drawing compass and ruler and show some interesting ideas of the algorithms of infinity.

## Christian Symbols

The most prominent Christian symbol is undoubtedly the cross. But there are a few other symbols that are all related to Sacred Geometry. Interestingly, most of these symbols are found beyond the realm of Christianity with a similar meaning behind it. Besides the cross there is also the Holy trinity symbol, the fish and the Monogram worth mentioning that are all related to Jesus as the key figure of the Christian faith.

## Judaism Symbols

The most prominent Jewish symbol is the Star of David, but there is more to explore in the book Torah. Again a symbol found all over the world, the Star of David has only recently been a strong symbol for Judaism as it is on the Israeli flat. With two interlocking triangles, this symbol has many meanings attached to it, such as the marriage of male and female or the unity of matter and spiritual world. Besides the Star of David, there is also the Kabbalah Tree of Life and the Merkaba that hold interesting meaning hidden within the geometry.

## Buddhist Symbols

Buddhism is about 2500 years old and is based on the teachings of Siddhartha Gautama who was preaching about the end of suffering. Buddhist symbols are found all around Tibet, India, in parts of China and Japan. Many Buddhist symbols also belong to Hinduism and Jainism. They share Om, the Dharma Wheel and the Swastika. Peculiar for Buddhism is the Buddha eyes, which represent ultimate knowledge and the third eye chakra. The Dharma Wheel with its eight-spokes holds, is related to the eight fold path and is one of the most important symbols of Buddhism.

## Hindu Symbols

Primarily spread in India, the roots of Hinduism are found in the oldest scriptures of the world, the Vedas. Core beliefs are the goals of life, which is morals, prosperity, passion and libration. Many Hindu symbols are imbued with spiritual meaning, which also overlap with Buddhism and Jainism. Many symbols are related to specific gods and goddesses. Saraswati, the goddess of knowledge and music, for example is often depicted with a book that depicts the Swastika and Om. She is the consort of Brahma, the creator, who has four faces and his symbol is the Swastika, which means luck. Another great symbol is the Star of Laxmi, which represents Laxmi, the goddess of wealth and abundance. Both of these symbols are based on a the 90° symmetry.

## Mandalas & Yantras

In India, we find Sacred Geometry in Mandalas and Yantras as objects of devotion in Buddhism, Hinduism, and Jainism. The word Mandala comes from Sanskrit, which means circle. A Mandala symbolises aspects of the Universe, while Yantra means vehicle and often represents deities in the Tantric traditions. Both are used as a schematic visual representation of the cosmos to help gain a higher state of consciousness. Internally, they act as a guide for several psychophysical practices such as meditation, prayer, healing and art therapy. In the West, Mandala colouring books have been a trend lately, helping people to reduce stress as a type of art therapy.

## Taoism Symbols

Taoism or Daosim is a Chinese philosophy or religious tradition that is attributed to Lao Tzu (c. 500 BCE). It emphasises living in harmony with the Tao, which is a Chinese word for path, way or principle. Its central teaching is based on the concepts that nature’s principles are in flow and are the source and the driving force behind everything that exists. It is about living life in harmony.

## Foundations

When we talk about the Sacred Geometry pattern, it actually refers to the expansion of overlapping circles, which creates a blueprint from which all other geometric forms, and spiritual symbolism can be created. According to the principles of Sacred Geometry, the patterns creates all dimensions from 0D to 3D, 4D, 5D and higher dimensions of space, time and consciousness itself. But before we go into the more scientific understanding of geometry, let’s explore the pattern itself and how it evolves from just a drawing compass and ruler.

## The Dot

Sacred geometry begins as a dot or point, which equates to a closed drawing compass. The dot that we normally draw on a piece of paper will only conceptualise the dot, but is not the dot itself, as the dot does not exhibit space, but defines a point in space, i.e. 0D. We refer to it as the concept of infinity in, just like a blackhole or the idea that gravity pulls the mass of the Earth towards its centre. Being the infinity within itself, a dot represents a contractive force going inwards forever. Just as the Big Bang theory suggests that our Universe started from a Singularity (an infinite dense dot, beyond space, time). A dot will always define the centre of infinite space. From a spiritual point of view, the dot can be seen as consciousness itself, the centre of our own being, the still observer or oneness consciousness.

## The Line

The Line

The first dimension, the Line, comes into being as the dot divides into two, just as we open the drawing compass to create the radius of a circle. A Line has no thickness and is the first space that can be created between two dots, 1D. We see it as the horizon line, which is only the difference between the sky and the earth. In Sacred Geometry, it is important to note that this first line is referred to as one, no matter how long the actual measurement is. This is another reason why Sacred Geometry is considered ‘sacred’ as we do not have any measurements, only ratios and proportions that come out of our original compass opening, ONE.

## The Circle

When we keep one dot stationary and rotate the other dot with our drawing compass, we can generate the next dimension, 2D, which is a circle. The process of rotation is indeed expressed throughout the Universe, with the earth rotating around its axis, rotating around the sun, the solar system rotating around the galaxy. Very often when we make a dot on a piece of paper, it looks like a small circle. Indeed, the dot and circle are intimately connected, in fact they are the opposite of each other, we call it inverse geometry. If the dot is a force of contraction, then the circle is a force of expansion. Just as we throw a stone in water (dot), the water will create circular ripples that expand outwards and dissipate into infinity (circle). We can place any other 2D shape inside a circle, yet the circle itself is the all-encompassing form with an infinite number of corners. Therefore, it is also often referred to as the Womb of Creation.

## The Vesica Piscis

From two equally overlapping circles, we get the ‘Vesica Piscis’, which is the overlapping area that looks like an almond shape, another name for it is ‘Mandorla’. Literally translated into ‘fish’s bladder’, this symbol is very prominent symbol in christianity related to Jesus. It also appears in other sacred places such as the Chalice Well in Glastonbury or as a symbol for the third eye in the Vedic Chakra System. The circles intersect each other and create two new points, also termed ‘Nodes’. In Sacred Geometry, we only ever work with nodes. In nature, we find the Vesica Piscis in plants, in the pattern of water ripples, planet explosions, atomic waves and even as the shape of the human eye.

## 2D Geometry

In the next part we examine the 2D forms that are commonly found within the practice of Sacred Geometry. Each image holds information that can be incorporates specific ratios. however only shapes that conform to the triangle-hexagon or square are able to tile a 2D plain to form a regular tapestry. All other shapes require the addition of a to or more shapes to fill in the spaces of the tessellation.

## The Trinity

From the Vesica Piscis, we can go to one of the nodes and add another circle without changing the original radius. This process will create a form called the ‘Trinity’, ‘Triad’, ‘Tripod of Life’ or ‘Triquetra’, which was mentioned in religious symbolism. Geometrically, the trinity is the template for an equilateral triangle, when we connect the nodes together, the smallest 2D form that exists. At the same time, we also find that the trinity draws out the template of the smallest 3D form, the Tetrahedron, when we fold the triangle into 3D space. Three is a limitation factor throughout nature that holds a certain property in space.

## The Trion Re

Just as we created a circle from one of the nodes of the Vesica Piscis to form the trinity, we can add another circle on the other node and bring perfect balance into the image, forming the Trion Re. The Trion Re is the small pedal shape that is now created from four overlapping circles. from the four nodes, we can create a 90° cross. The Cross is a religious symbol and is also related to our experience fo reality as well as electromagnetic waves.

## The Seed of Life

Following the principle of Sacred Geometry, six circles will fit perfectly around a central seventh circle to give rise to a flower-like pattern. This image is known as the ‘Seed of Life’. The name has been popularized by spiritual teacher Drunvalo Melchizedek in his books and workshops since the 1920’s. Yet its appearance goes way back known as ‘rosette patterns’ found extensively in Europe, Asia and North Africa. One of the earliest examples is in Greece about 400 BC. The principle of 7 can be found in the 7 days of Creation within the book of Genesis, therefore the Seed of Life is sometimes referred to as the ‘Genesis Pattern’. Just as there are 6 circles around 1, there are 6 days of creation with the 7th on which ‘God rested’. The limitation of 7 also reflects in the 7 notes in the musical scale, 7 vedic chakras, 7 days of the week, 7 shells in the Atom. In our latest research, we discovered that the Seed of Life is the turning point from which 2D can transform into 3D via three axes, x, y, and z into the Octahedron.

## The Egg of Life

The Seed of Life can be expanded by one round of 6 more circles to form a total of 13 circles known as the Egg of Life. The Egg is always considered as a symbol for fertility and rebirth. When you see it as a three dimensional object and blend the background circles, it visualises 8 spheres arranged in cubic formation. This is specifically interesting when we observe how the first cells of any mammal undergo the process of embryonic development. On the third day, the cells are in an 8-cell stadium arranged just like a cube after which, the cells start to divide rapidly. The Egg of Life maps the crucial point where cellular transformation occurs.

## The Flower of Life

The Flower of Life succeeds the Egg of Life with 6 more circles, completing the next level of information to a total of 19 circles. It is the central symbol of Sacred Geometry. The oldest inscription was found in Abydos, Ancient Egypt. about 4000BC. It also appears underneath the claw of the Lion on the entrance of the forbidden city in Beijing, China, the protector of knowledge. Many healers use the symbol in their ceremonies, where it is seen as the energetic blueprint underlying reality, just as we have DNA coding all proteins and processes of the cell and ultimately our body. As the Flower of Life naturally forms the triangular and hexagonal tessellation, it works as 2D Boundary to separate out 3D space. When the Flower of Life expands to 37 it reaches the Moonflower, then 61, the Flower of Heaven. We have invented both of these terms to distinguish the different stages of expansion within the Flower of Life. With every set of circles, more information is revealed.

## The Fruit of Life

When the Flower of Life expands to 43 circles, we reach the first manifestation of another layer of 13 full circles, called the Fruit of Life. Just as the Egg of Life, counting 13 overlapping circles, the Fruit of Life has 13 full circles in 2D, while the Cuboctahedron nests 13 spheres in 3D space, the respective pattern on different levels of information. Expanding to the Flower of Heaven (61), the background energetic blueprint completes. The link to the Atomic structure is interesting as element 43, Promethium and 61, Techneticum are insatiable and do not exist in nature.

## Metatron's Cube

When we connect each centre of every single circle of the Fruit of Life with each other, we get a complex image called the Metatron’s Cube. Related to the Archangel Metatron, this spiritual symbol is known to encode the shadow project of all 5 Platonic Solids. What many do not know is that is also maps the Archimedean Solids and the Electron Cloud of the Atom, i.e. the foundations of matter.

## 3D Solids

The practice of Sacred Geometry can also be applied to 3D polyhedra. From a foundation of 5 regular Platonic solids, the 13 Semi-regular Archimedean solids are derived. Certain polyhedra such as the Star-Tetrahedron and Octahedron, are often used in meditation techniques, such as the Merkaba meditation.

## 5 Platonic Solids

The 5 Platonic Solids that are mapped within the Metatronscube are the only 3D regular polyhedra that fit inside of a sphere. Their characteristic is that they each consists of the same face, triangle, square or pentagon, and are in complete equilibrium. The Octahedron, Tetrahedron, Cube, Octahedron, Dodecahedron and Icosahedron are unique for 3D space, as we cannot create any more shapes that have the same characteristics. Rediscovered by philosopher Plato of Ancient Greece, the 5 solids were seen as the foundations of the Universe and are often related to the 5 elements, fire, water, earth, air and aether (electricity). In light of today’s discoveries of the atom, we have relabelled their relationship to the five elements and came up with a fantastic model that fits not only space and the atom but also the earth and even the solar system.

## 13 Archimedean Solids

The Archimedean Solids named after Greek philosopher Archimedes, are an extension of the 5 Platonic Solids. Unlike the Platonic Solids, they consist of two or three different faces, the triangle, square, pentagon and hexagon. Through truncation, explosion and twisting, the Platonic Solids can transform into the 13 Archimedean Solids and bring 3D space up to 18 plus the sphere. We see that space gains more complexity now. One of the most prominent Archimedean solids is the Cuboctahedron. Tt is a shape that has been extensively studied by many people such as Buckminster Fuller. It is in that sense unique as it nests 13 spheres in space. the 12 vertices are exactly the same distance to the centre, which means that it is the only Archimedean Solid that fits inside a sphere, the Vector equilibrium. Just as the Seed of Life nests 6 circles around one, the Cuboctahedron nests 12 spheres around 1 and expands space to the next scale.

## 4D Geometry

When we think about the nature of 4D polyhedra it is quite normal to believe that they are beyond the ability of our 3D constrained minds to conceptualise. However, by understanding the basic principles whereby these 4D forms can present themselves, then the whole process can be simplified. In its simplest interpenetration, a 4D polyhedra can be envisioned as two of the same shape occupying the same 3D space. Often when producing a conceptual model we reduce one the the shapes in size so that we can appreciate the difference between the two. In the next part we will examine some of the most common 4D forms that are applicable to Sacred Geometry.

## The Torus

When a dot becomes a circle and a circle, a dot, it is called Inverse Geometry. If this happens in 3D space, we get a shape called the torus, which looks like a donut. In mathematics, the fourth dimension is usually defined as time. The torus is the first shape that incorporates that quality as it is a moving shape, i.e. the dot moves into another space, the sphere. It is 4D as something can exists inside and outside simultaneously. The Universe is made from Toruses as we see it on every scale from the Atom to the Galaxy, the electromagnetic field of the Earth and even the so-called Aura of every being.

## The Hypercube

Similarly to the Torus, the Hypercube or Tesseract consists of a Cube that swaps with another cube and is in this way also related to time. We see this shape as the process by which one moment of time is transformed into the next, just like a movie of 3D pixels that move from frame to frame.

## 5D & Beyond

Just as 4D polyhedra can be conceived as being composed of two 3D polyhedra that occupy the same 3D space, so the concept can be extended to higher dimensions. 5D shapes are often envisioned as three polyhedra superimposed over one another. Often these are set in motion around a central axis, whereby two of the polyhedra rotate in opposite directions, whilst the third remains fixed in place. It is this rotation in two opposing directions that balances the form when used in meditation practices.

## Double Torus

Just as a Torus is a 4D shape, a Torus connected to a Torus is a 5D shape. It consist as the energetic system of our heart and also in the F-orbitals of the Electron cloud in the Atom.

## 5D Hypercube

A 5D Hypercube can be envisioned as 3 cubes superimposed over the same space. Often this is visualised in 3D as a set of three cubes nested inside of one another. Within the structure of the electron cloud there a three D-orbital electron sets. In Atomic Geometry these are often defined using a cubic space. Interestingly, the cube at the centre of the set of three exhibits a anomalous non-stable element (Technetium 43) at exactly halfway through its formation.

## 5D Merkabah

As mentioned previously, the Merkaba is a spiritual symbol, a vehicle of consciousness acceleration. The meditation technique of the Merkaba is actually a 5D experience. Three of them overlay each other and are brought into rotation in opposite directions with one Merkaba being stationary. This in turn activates that spiritual vehicle around you and elevates the energy, some people even experience an uplifting sensation fo their bodies being i this meditation.

## Sacred Geometry in Nature

Natural forms are often expressed in terms of fractals, self-repeating patterns. These can be approximated through geometric constants such as the Golden Ratio, Fibonacci numbers, or tapestries constructed from regular form. Popular ideas include the hexagonal structure of the honeycombs, the spiral shape among nautilus shells, hurricanes, whirlpools, tidal waves etc. The theme continues throughout the plant kingdom, where regular shapes produce the arrangement of petals in a flowers, Fibonacci spirals often determine the 3D form of many fruits and seeds. In fact, the Fibonacci sequence and the Golden Ratio is so ubiquitous that it can literally be found in anything that lives and breathes, including humans.

## Fibonacci Spiral

In nature, we see many spirals in flowers, in fruits such as in a pineapple, in the flowering of artichokes, the arrangement of pine cones or the way waver breaks. These spirals are based on the Fibonacci sequence named after Italian mathematician known as Fibonacci. Yet, there is evidence, it seems to appear in the ancient scripture of India. The pattern follows the simple principle of addition of the last two numbers, starting with 1 and 1 which follows: 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 (the last number occurring in a sunflower) and so on. In terms of Sacred Geometry, we can express the sequence in squares that creates the spiral we see around us. Interestingly, the starting point is 6 squares within the Vesica Piscis.

## The Golden Ratio

The Fibonacci series is intimately related to what is known as the Golden Ratio, the Golden Section or Golden Mean. The higher the Fibonacci numbers, the closer they approach the Golden Ratio, Phi or Φ (1,618…). The unique feature is the fact that it can grow or shrink, always containing the same ratio, that is why it is also called the divine proportion. We find this number everywhere in nature and within the Human body such as the proportions of our hand to our elbow. In terms of geometry, the Golden ratio naturally exists within the pentagon. It can also be created form the square and the triangle, which all come out of the Sacred Geometry pattern.

## The Silver Ratio

Similar to the Golden Ratio, we find the Silver ratio, which relates to √2 and the Octagon. We find the Silver Ratio in certain Galactic Spirals, which can be mapped out by the Archimedean Solid, the Rhombicuboctahedron.

## Fractals

Fractals are intricate self- similar patterns that express themselves infinitely from large to the small. Examples of Fractals in Nature are the Romanesco broccoli, the patterns of tree branches or crystal formations. They are created by repeating a simple process over and over in an ongoing feedback loop. Fractals hold the concept of infinity within themselves, great examples are the famous Mandelbrot Set, the Sierpinsky Triangle or the Koche Curve. A fractal may look like a complex shape and it is infinitely complex, yet at the same time it an be generated from simple shapes such as a triangle, a square or a pentagon. Naturally, the pentagon creates a pentagon – pentagram fractal going into infinity within itself and without, while the triangle and square need to be transformed in order to create the infinity in and out.

## Sacred Geometry in Science

Even though Sacred Geometry is mainly associated with pretty symbols and spiritual meaning, there is more and more evidence that the phenomena we observe in Quantum Physics, Chemistry, Biology to Cosmology also follows the same geometric principles. Here are a few example, where Sacred Geometry is expressed in our scientific experimentation.

## Cymatics

When experimenting with sound and frequencies it becomes apparent that it is intimately related to shape. Known as Cymatics, which translates into wave from Greek, it deals with vibrational phenomena. This field of research focusses on the shape of sound where water or sand is usually on the surface of a plate which is being exposed to vibrations. Similar observations are found by Japanese scientist Dr. Masuroto. He studied the the crystallisation after being exposed to vibration and demonstrated that positive intention, harmony creates beautiful Mandalas, while negative words create chaos.

## The Geometry of Light

In the spiritual realm there is much talk about energy and light (enlightenment), but what does this mean in terms of science? When we talk about (visible) Light it is part of the electromagnetic spectrum, which consists of two components, the magnetic and electric field that are exactly 90° oriented to each other, a Cross. That geometry is expressed in Electromagnetic fields can also be seen when we look at the Earth. Here we see the 4D Torus in action, i.e. a dot transforming into a circle and vice versa. The toroidal shape of the Electromagnetic field with its North and South pole express exactly the quality of the geometric form.

## Atomic Geometry

If we look at Quantum Physics, we are in the realm of Atoms. Ever wondered how the foundation of matter looks like? It looks like Geometry! Even though there seems to be a chaotic behaviour in the Electron cloud, it is apparent that this is limited by geometric symmetries. Each Atomic Oribtal (subshell) follows the simple principles of geometric shapes internally, such as the line, the square, and the hexagon. Seeing them as sets coming together, we find the Octahedron, Cube, Star-Tetrahedron, the Cuboctahedron, Rhombidodecahedron and Icosahedron. The way these geometries are nested and transform into one another, we call Atomic Geometry. The Atomic Blueprint builds the foundations of the Universe, which also appears on larger scales of the Universe.

## Molecular-Geometry

Atoms bond to each other to form molecules. The spacial geometric formation of Atoms also translates into Molecules known as Molecular Geometry. Even though not seen as 3D shapes in science, we can interpret the geometries again as part of known 3D solids such as the Methane, a Carbon atom binding to 4 hydrogens, forming a Tetrahedron. What comes more apparent in the field of Chemistry is the reason why Atoms want to form bonds with each other in the first place. According to the Octet rule, Atoms will always want to fill out their outer shell with 8 electrons, which equates to the Octahedron. Indeed, all non-reactive Atoms, the Noble gases such as Neon, always adhere to the Octahedron. The processes within cells and the larger cycles of life are all based on the transformation of shapes. Many crystals, stones, the cells of our skin, and plants follow obvious geometric formations, which all go back to the structure of molecules and atoms.

## Solar Geometry

Just as the atoms, the cells and our body follow symmetries and geometric shapes, even the planets of the solar system orbit at certain distances to each other. Based on the findings of one of the key figures of the 17th century scientific revolution, german astronomer Johannes Keplar, proposed a model of the solar system based on the nested set of 5 Platonic Solids. Even though he did not get famous for that and modern science had abolished these views, he never gave up his idea of a divine, geometric model of the Universe. Indeed, even today we find great accuracy in his predications if we take the mean orbits into account to about 95%. On top of that, the geometric relationship between the planets also find relations to the laws of music in the Music of the Spheres of Ancient Greece.

## Conclusion

##### About the Author

**In2Infinity established in 2015 by Colin Power and Dr. Heike Bielek.**