Geometric Shapes and Their Symbolic Meanings

Nautilus Shell Cross-Section, a naturally occuring spiral. Getty Images / WilshireImages
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Circles

Rings Grid
Dinamir Predov / Getty Images

Because basic geometric shapes are so simplistic in construction, they are found all over the world and have wide variety of uses and meanings. However, there are a variety of meanings that are more commonly ascribed to these shapes, particularly when used in a religious or magical context.

Circles commonly represent unity, wholeness, and infinity. Without beginning or end, without sides or corners, the circle is also associated with the number one.

In some cases, there is a distinction between that which is contained within the circle and that which lies without.

Protection

Circles are often seen as protective symbols. Standing within a circle shields a person from supernatural dangers or influences outside of the circle. Conversely, a circle can also be containing, keeping that which is inside from been released.

Ouroboros

The ouroboros is a circular symbol created by a creature feeding off it's own tail, or else two creatures feeding off each other's tails. In both cases, the shape created in a circle, represents such ideas as completion, uniting of polarities, regeneration, and eternity.

Sun Symbols

Circles are frequently used as sun symbols, as well as representing things associated with the sun. The astrological symbol of the sun is a circle with a dot in the middle. The same symbol is often used to represent gold, which is strongly associated with the sun.

The Element of Spirit

The element of spirit, seen as an element equal or superior to the physical elements of fire, air, water and earth, is commonly represented by a circle.

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Spirals

Spiral Aloe. Getty Images / Mady Reichenbach / EyeEm

Spirals are some of the oldest geometric shapes in ancient artwork, dating back at least to the Neolithic period. As such, we know very little about their religious beliefs and can, at best, guess about general meanings of symbols based on context.

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Triangles

Golden triangular terraces in modern architecture. Golden Terraces in Warshaw. Getty Images / Krakozawr

In Western society, the triangle most often has highly Christian meanings when used in a religious context. Because the Christian God is a trinity - Father, Son and Holy Ghost united in a single godhead – he is commonly represented by a triangle.

As a three-sided polygon, the triangle represents the number three, which is meaningful to many groups. As such, triangles and other symbols made of three parts may be used to present such concepts as past, present, and future or spirit, mind and body.

As a Summoning Symbol

Some occultists use the triangle as a summoning symbol. At the culmination of a ritual, the desired being is expected to appear within a triangle inscribed upon the floor. The occultist often performs his ritual from the protection of a circle.

Point-up and Point-down Triangles

The orientation of a triangle can be important to it's meaning. For example, a point-up triangle might represent a strong foundation or stability, as it is rooted to the ground through a solid base.

The elements of earth and water formed from point-up triangles, even thou these are the two more material elements. Symbols for air and fire are formed from point-down triangles.

The point-up triangle can represent male energy, and fire and air are masculine elements. The point-down triangle can represent female energy, and water and earth are feminine elements.

Point-up triangles can also represent ascension toward the spiritual world, while the point-down triangle can represent a descent into the physical world.

The uniting of a point-up and point-down triangle creates a hexagram.

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Crosses

Low Angle View Of Cross Against Sky. Getty Guido Menker / EyeEm Creative

The cross is most well-known in its Christian context as a symbol of sacrifice and salvation in reference to Jesus's death by crucifixion upon a cross. However, the cross has numerous other religious meanings as well, most of which have to do with groups of four, corresponding to the four points on the cross.

Crosses very commonly represent the earth and the physical universe, particularly in Western culture. This comes primarily from two associations: the four physical elements (earth, water, air and fire) and the four cardinal directions (north, south, east and west). Indeed, the astrological symbol for Earth is a cross inside a circle. The same symbol is also known as a sun cross or solar wheel and has been associated with the sun and its four seasons.

Crosses share many properties with squares, which tend to have even more material meanings than crosses.

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Squares

Full Frame Shot Of Colorful Blocks. Getty Images / Credit: Roan Gumangan / EyeEm

Because the number four is commonly associated with material things—the physical elements, the directions of world, the seasons of the world—both squares and crosses are often used as symbols of the material world itself. However, a square has a visual solidness that a cross lacks. A square has volume. It contains space. 

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Pentagram - Five-Pointed Star

Close-up of stars mounted on the wall at a war memorial, Freedom Wall, National World War II Memorial, Washington DC. Getty Images / Panoramic Images

The five-pointed star, also commonly called a pentagram, has been in use for thousands of years by a variety of cultures. Most uses of the pentagram in Western society today descend from Western occult traditions. The pentagram is also the official symbol of the Baha'i Faith.

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Heptagrams / Septagrams

Acute Heptagram Septagram
Catherine Beyer

Seven-pointed stars are known as heptagrams or septagrams. There are two different configurations for heptagrams, the acute heptagram, shown here, and the obtuse heptagram. In addition, the heptagon – a seven-sided polygon – can also represent the same things as a heptagram.

Astrological Significance

The ancient world recognized only seven planets: Mercury, Venus, Mars, Jupiter and Saturn, plus the Moon and Sun. (Uranus, Neptune and Pluto are not visible to the naked eye and thus were unknown.) The heptagram often reflects these seven planets.

This is particularly important in western occultism, where systems of correspondence were often based upon astrological correspondences. It was understood that each planet radiated certain influences. Understanding those influences directly is the realm of astrology.

But it was also accepted by many occultists that those influences were soaked up and re-projected by items that had connections with specific planets. For example, gold radiated success and perfection precisely because it corresponded to the sun, which radiates the same qualities.

Universal Balance

Because the planets are all represented equally in the heptagram, the symbol can also be one of balance, equally representing the seven great powers of planetary magic.

Furthermore, the pairing of the numbers three (spirituality, in reference to the Christian trinity) and four (physicality, in reference to the four elements and the four cardinal directions) can also represent universal balance.

Orientation can sometimes be important here. The points over four can symbolize spirit ruling matter, while four points over three can be physicality ruling spirit.

Days of the Week – Symbol of Completion

The heptagram can also represent the seven days of the week. In Judeo-Christian context, it can therefore be a symbol of completion, as the universe was wholly created within the seven-day week.

Elven Star

The acute heptagram is sometimes called the Elven Star or the Faerie Star and has been widely adopted by the Otherkin – people who believe they are supernatural beings such as elves, faeries or dragons trapped in human bodies.

Enochian Angel Magic

Heptagrams and heptagons are commonly used in John Dee's system of Enochian angel magic, which is strongly rooted in sets of seven. The most famous example is Dee's Sigillum Dei Aemeth.

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Obtuse Heptagram

Obtuse Heptagram Septagram
Catherine Beyer

Seven-pointed stars are known as heptagrams or septagrams. There are two different configurations for heptagrams, the obtuse heptagram, shown here, and the acute heptagram. In addition, the heptagon – a seven-sided polygon – can also represent the same things as a heptagram.

Read more: General Meanings for Heptagrams

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Heptagram Correspondences - Days of the Week and the Seven Planets

Heptagram Septagram
Catherine Beyer

The heptagram can represent the seven days of the week. In Judeo-Christian context, it can therefore be a symbol of completion, as the universe was wholly created within the seven-day week.

In addition, the each day of the week is associated with one of the planets.

By following the circle counter-clockwise, starting at the moon, you find that the planets are listed in the order in which they were understood to exist in an earth-centric system: Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn.

By following the lines of the acute heptagram, you find them listed in the order of the days of the week: Moon (Monday), Mars (Tuesday), Mercury (Wednesday), Jupiter (Thursday), Venus (Friday), Saturn (Saturday) and the Sun (Sunday).

Read more: Additional Meanings for the Heptagram

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Hexagram

Hexagram

A hexagram with equidistant points is unique in geometry because it cannot be drawn unicursally – that is, without lifting and repositioning the pen. Instead, overlapping two individual triangles forms the hexagram.

A unicursal hexagram is possible – the creation of a six pointed shape without lifting the pen – but the points will not be equidistant from one another.

For more information, please see the full article about the hexagram.

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Unicursal Hexagram

Unicursal Hexagram

The unicursal hexagram is a six-pointed star that can be drawn in one continuous movement. Its points are not equidistant, and the lines are not of equal length (unlike a more standard hexagram). It can, however, fit inside a circle with all six points touching the circle.

The unicursal hexagram is commonly depicted with a five-pedaled flower in the center. This is a variation created by Aleister Crowley, and is most strongly associated with the religion of Thelema. Another variation is the placement of a small pentagram in the hexagram's center.

For more information, please see the full article about the hexagram, which includes a diagram about how to construct a unicursal hexagram

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Enneagram - Fourth Way

Enneagram used by the Fourth Way
Enneagram used by the Fourth Way. Catherine Beyer

The term enneagram today is actually most associated with an approach to personality analyzing and development. It centers of the idea of there being nine personality types which are diagrammed into an irregular nine-pointed shape. The lines represent connections and relationships between the types and locations around the circle give additional insight.

That same nine-pointed shape was used in a branch of thought known as the Fourth Way, which developed in the mid 20th century.

Fore more usages of 9-pointed stars, as well as other complex polygons and polygrams, click here.

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Enneagram of Overlapping Triangles

Enneagram of Overlapping Triangles
Catherine Beyer

An enneagram is a nine-pointed star. When the enneagram is formed by three overlapping triangles, it may represent a trinity of trinities and, thus, be a symbol of holiness or spiritual completion.

It is possible someone might use an enneagram as a symbol of universal wholeness with each point representing a planet, although the downgrading of Pluto from planet to plutoid now complicates such symbolism.

For more usages of 9-pointed stars, as well as other complex polygons and polygrams, click here.

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Baha'i Enneagram

Baha'i Enneagram

While the five-pointed star is the official symbol of the Baha'i Faith, the nine-pointed star is more commonly associated with the religion, even being used as the representative symbol on the official US website for the faith. There is no standard format for the star; as depicted here, it is constructed of three overlapping equilateral triangles, but equally valid depictions can use either sharper or shallower angles to the points. The preferred orientation is point-up.

For the complete article on the Baha'i symbol, click here

For the Baha'i Symbol Gallery, click here.

Fore more usages of 9-pointed stars, as well as other complex polygons and polygrams, click here.

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Decagram/Dekagram

Decagram from overlapping pentagrams
Catherine Beyer

For those working within a Kabbalistic system, the decagram can represent the 10 sephirot of the Tree of Life.

A decagram can specifically be formed by overlapping two pentagrams. This can reflect the union of opposites, as point-up and point-down pentagrams can each have their own meanings. A pentagram can represent the five elements, and some see each element as having a positive and negative aspect. As such, any decagram (not just one made by overlapping pentagrams) might also represent the positive and negative aspects of the five elements.

Read more: Complicated Polygons and Stars

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Dodekagram

Dodekagram from four overlapping triangles
Catherine Beyer

The number twelve has a lot of potential meanings. It is the number of months in the year, thus representing a yearly cycle and its completion and wholeness. It is the number of disciples of Jesus, which makes it a common number in Christianity, and the original number of Hebrew tribes, which makes it a common number in Judaism.

But a twelve-sided figure most commonly represents the zodiac, which is divided into twelve signs. Those twelve signs are further divided into four groups identified by element (three fire signs, three water signs, etc.), so a dodekagram made up of four overlapping triangles (depicted here) works particularly well. A dodekagram made up of two overlapping hexagons (depicted here)can be used to divide the zodiac symbols by male and female qualities. (You can't overlap hexagrams, since hexagrams are overlapping triangles. It's the same thing as a dodekagram made up of four triangles.)

Read more: Complicated Polygons and Stars

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Dodekagram - Overlapping Hexagons

Dodekagram with two hexagons
Catherine Beyer

The number twelve has a lot of potential meanings. It is the number of months in the year, thus representing a yearly cycle and its completion and wholeness. It is the number of disciples of Jesus, which makes it a common number in Christianity, and the original number of Hebrew tribes, which makes it a common number in Judaism.

But a twelve-sided figure most commonly represents the zodiac, which is divided into twelve signs. Those twelve signs are further divided into four groups identified by element (three fire signs, three water signs, etc.), so a dodekagram made up of four overlapping triangles (depicted here) works particularly well. A dodekagram made up of two overlapping hexagons can be used to divide the zodiac symbols by male and female qualities. (You can't overlap hexagrams, since hexagrams are overlapping triangles. It's the same thing as a dodekagram made up of four triangles.)