Geometric Shapes and Their Symbolic Meanings

Forms ranging from circles to dodekagrams have significance in many philosophies

Geometric shapes—triangles, circles, squares, stars—have been part of human religious symbolism for thousands of years, long before they became part of scientific endeavors and construction projects by the Egyptians and Greeks. The simplest shapes are found in nature and are used by many different cultures around the world to represent a wide variety of meanings. Shape symbols range from common circles and squares and triangles to more obscure shapes such as unicursal hexagrams.

The 6th century BCE Greek philosopher and mathematician Pythagoras believed that geometry was the rational understanding of God, man, and nature: Many of the shape meanings in western philosophies arise from his writings. Various meanings are commonly ascribed to these shapes, particularly when used in religious or magical contexts.

Circle

Rings Grid
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Circles are among the oldest of geometric symbols, and commonly represent unity, wholeness, and infinity. Pythagoras called the circle "monad," the most perfect of creative forms, without beginning or end, without sides or corners. He associated the circle with the number 1 and the practice of monotheism.

Perfection and Ideals

In the Zen Buddhist philosophy, a circle stands for enlightenment and perfection in unity with the primal principles. Circles are sometimes symbols of the Judeo-Christian God and sanctity, appearing as haloes. In Chinese symbology, the circle represents the heavens.

Circles are also often seen as protective symbols. In occult practices, standing within a circle shields people from supernatural dangers or outside influences. Circles can also represent containing, keeping what is inside from been released.

Ouroboros

The ouroboros (Greek for "tail swallower") is a circular symbol representing a snake or dragon feeding off its own tail, or two such creatures feeding off each other's tails. First attested in the New Kingdom Egypt in the 10th-11th century BCE, the ouroboros represents the cycle of rebirth, completion, unification of polarities, regeneration, and eternity. Ouroboros is also found in Aztec and Norse mythologies.

Sun Symbols

The circle is also used nearly universally to represent the sun and/or the moon, or things associated with those bodies. The astrological symbol of the sun is a circle with a dot in the middle. The same symbol is used to represent gold, which is strongly associated with the sun.

Element of Spirit

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

Spiral

Spiral staircase
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A spiral is a curve that starts as a point in the center, and curls around to a large circle; concentric circles are related symbols, consisting of a set of nested circles. Found in nature such as nautilus shells, spirals are some of the oldest geometric shapes, found carved into Neolithic passage tombs in the United Kingdom, carved on rock art around the world, and as part of the geoglyphic Nazca lines in Peru.

Anthropologists and others typically associate spirals and concentric rings with shamanism and the achievement of altered states of consciousness.

Triangle

Golden triangular terraces in modern architecture

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In Western society, equilateral triangles most often have Christian meanings in religious contexts. Because the Christian God is a trinity—Father, Son, and Holy Ghost united in a single godhead—he is commonly represented by a triangle.

Pythagoras associated the number 3 with triangles, which is meaningful to many groups. Triangles and other three-part symbols may present such concepts as past, present, and future or spirit, mind, and body.

Summoning Symbols

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 rituals from the protection of a circle.

Point-Up and Point-Down Triangles

The orientation of a triangle can be important to its meaning. Point-up triangles represent a strong foundation or stability. Earth and water symbols are formed from point-up triangles; pointing upward stands for the ascent to heaven. The point-up triangle can also 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. Symbols for air and fire are formed from point-down triangles; point-down triangles can represent the descent into the physical world.

When paired and presented as point-to-point, triangles represent sexual union and the principle of harmony. Intersecting point-up and point-down triangles creates hexagrams.

Cross

Low Angle View Of Cross Against Sky

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The cross is best known in its Christian context as a symbol of sacrifice and salvation referring to Jesus' death by crucifixion. The cross has numerous other religious meanings, most of which reflect groups of four, corresponding to the four points on the cross.

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

Crosses share many properties with squares, which usually have more material meanings than crosses.

Square

Colorful Blocks

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Pythagoras associated the square with the number 4, and that number in many cultures is commonly associated with material things—physical elements, compass directions, and seasons. Thus, squares and crosses are often used as symbols of the material world. However, squares have visual solidness that crosses lack. A square has volume; it contains space. 

Squares represent solidity, a perfection that is static, dependable, earthly and material. In Hinduism, the square represents cosmic order and the balance of opposites; in Native American religions, the square represents permanence, a safe place. In Chinese symbolism, the square represents the earth. In many many cultures, a square is a meeting place, a plaza at the heart of a city.

Pentagram

Close-up of stars mounted on the wall

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The five-pointed star, called a pentagram, has been used for millennia by a variety of cultures. Five-pointed stars are found in Mesopotamia from the 4th millennium BCE; stars are used in conjunction with a crescent to represent Islam. Muhammad said that the star represented "our smiling hope, the beauty of aim and object, and the light of our belief in God."

Most uses in Western society descend from occult traditions, and in Wicca, the pentagram is a symbol of protection and warning, while in Satanism it represents the Goat. Pythagoras associated the number 5 with the star; the Mah Jong tiles marked a five-pointed star represents the number 6.

To Pythagoras, a five-pointed star represented the five elements that make up humans: fire, water, air, earth, and spirit. The pentagram is also the official symbol of the Baha'i faith.

Heptagram / Septagram

Acute Heptagram Septagram
Catherine Beyer

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

Astrological Significance

The ancient world recognized only seven "planets" other than Earth: Mercury, Venus, Mars, Jupiter, and Saturn, plus the moon and sun. Uranus, Neptune, and Pluto are not visible to the naked eye and thus unknown. The heptagram often reflects these seven planets, and in western occultism, systems were often based upon astrological correspondences of these seven points. It was believed that each planet radiated certain influences. Understanding those influences is the realm of astrology.

Universal Balance

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

Seven combines pairing the numbers 3 (spirituality, referring to the Christian trinity) and 4 (physicality, referring to the four elements and the four cardinal directions), which can also represent universal balance.

The orientation of the seven-point start can also be important in the occult world. Three points over four can symbolize spirit ruling matter, while four points over three can be physicality ruling spirit.

Days of the Week

The heptagram can represent the seven days of the week. In the Judeo-Christian context, it can be a symbol of completion, as the universe was 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're supernatural beings such as elves, fairies, 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.

Hexagram

Hexagram

 Catherine Beyer

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

The six-pointed star is a mandala symbol found on south Indian Hindu temples, symbolizing the perfect meditative state of balance. The six-pointed Star of David symbolizes God's rule over the universe, and in the Mormon church is symbolizes God reaching towards humans and humans reaching towards God.

A unicursal hexagram—creating a six-pointed shape without lifting the pen—is possible, but the points will not be equidistant.

Unicursal Hexagram

Unicursal Hexagram

 Catherine Beyer

The points of the unicursal hexagram, a six-pointed star that can be drawn in one continuous movement, are not equidistant and the lines are not of equal length (unlike a 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-petaled flower in the center, a geometric variation created by Aleister Crowley and associated with the religion of Thelema. Placement a small pentagram in the hexagram's center is another variation.

Enneagram of Overlapping Triangles

Enneagram of Overlapping Triangles
Catherine Beyer

An enneagram is a nine-pointed star, often associated with a branch of thought known as the Fourth Way, which was developed in the 20th century. Formed by three overlapping triangles, it can represent a trinity of trinities, a symbol of holiness or spiritual completion.

An enneagram might also be used as a symbol of universal wholeness, with each point representing a planet, although the 2006 downgrading of Pluto to a dwarf planet complicates such symbolism.

Baha'i Enneagram

Baha'i Enneagram

 Catherine Beyer

While the five-pointed star is the official symbol of the Baha'i faith, the nine-pointed star is commonly associated with the religion and is used as the representative symbol on its U.S. website. There is no standard format for the star. It is depicted here 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.

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 be formed by overlapping two pentagrams. This reflects the union of opposites, as point-up and point-down pentagrams have their own meanings. A pentagram can represent the five elements, and a decagram might represent the positive and negative aspects of all the elements.

Dodekagram

Dodekagram from four overlapping triangles
Catherine Beyer

The number 12 has many potential meanings. It is the number of months in the year, representing a yearly cycle and its completion and wholeness. It is the number of Jesus' disciples, making it a common number in Christianity, and the original number of Hebrew tribes, making it common in Judaism.

But a 12-sided figure most commonly represents the zodiac, which is divided into 12 signs. Those 12 signs are divided into four groups identified by elements (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.

Sources

  • Chwalkowski, Farrin. Symbols in Arts, Religion, and Culture: The Soul of Nature. Newcastle: Cambridge Scholars. 2016. 
  • Fontana, David. The Secret Language of Symbols: A Visual Key to Symbols and Their Meanings. San Francisco: Chronicle Books. 2003