The Union of the Hexagon and Pentagon

An elegant geometric solution to the problem of unifying the Hexagon and Pentagon by means of the Vesica was published by Albrecht Dürer in his Course in the Art of Measurement with Compasses and Ruler. It was subsequently republished in Charles Bouleau’s The Painters Secret Geometry and in John Michell’s The City of Revelation. It is an especially potent exercise in Sacred Geometry that serves to illuminate for the student the bridge linking form with meaning and is reproduced below:

Pentagonal geometry of the rose

Hexagonal geometry of the Lily

In contemplating the symbolism of hexagon and pentagon we note that flowers can display polygonal geometries in the configuration of their petals. Roses typically have their petals arrayed in whorls of five.

Several species of lily have their petals arranged in whorls of six, or two whorls of three petals each.

Roses were considered by the Egyptians to be sacred to the goddess Isis. By the Greeks roses were associated with Aphrodite (Venus), goddess of love. Myth describes how a rose bush grew from a pool of blood spilled by Adonis, who was Aphrodite’s lover. Medieval Christians associated the petals of the rose with the five wounds of Christ’s passion. It was also viewed as a symbol of both blood and the Virgin Mary. In Persia roses were given a prominent place in geometrical gardens. In some cultures roses are offered as gifts on the feast day of St. George. (May 6) To occultists and hermeticists the rose was a symbol of secrecy, from whence comes the saying “under the rose” or in its original Latin ‘sub rosa’ which perhaps originates with the Roman practice of hanging roses above the table around which a clandestine meeting was held, or at the door of the room in which the meeting took place. In ancient Greece candidates for initiation into the Mysteries wore roses to indicate that they would keep inviolate the secrets intrusted to them. Also according to occultists the rose vibrates at the highest frequency of any flower, and, not infrequently, those who have been witnesses to celestial visitations from the Goddess have reported detecting the fragrance of roses. When united with the cross the rose becomes a symbol of immortality and the transmutation of the human soul. Manly Palmer Hall in his Secret Teachings of all Ages remarks that “The rose is a yonic symbol associated with generation, fecundity, and purity. The fact that flowers blossom by unfolding has caused them to be chosen as symbolic of spiritual unfoldment . . . The number of its petals being ten is also a subtle reminder of the perfect Pythagorean number.” (Rose petals can be arrayed in multiple whorls of 5 each, two arrays equals ten petals)

The Lily or liles (also lotus) are said by the Greeks to be created from the breast milk of Hera, goddess of marriage and childbirth and therefore associated with motherhood. As the mythic tales recount Hercules was born of Zeus’s extramarital affair with a mortal woman and Zeus sought to have him become fully a god. To accomplish this the infant Hercules would have to suckle at the breast of a goddess. For this purpose Hera, the wife of Zeus was unknowingly recruited by being put into a deep sleep by Somnus, the god of sleep. However, the force of Hercules suckling was so great that the milk overflowed into a stream that flowed heavenward to become the Milky Way. Some drops of her milk also fell to Earth to become a white lilies. Another to some traditional beliefs lilies sprang up from the tears shed by Eve as she left the Garden of Eden in exile. Whereas Christian traditions represented the rose as being born out of the blood of Christ, the Easter lily sprang forth from his sweat. By contrast the lily also has a strong masculine connotation as well, as evidenced by the prominent stamens. The water lily is the counterpart of the Lotus, a flower of deep mystical significance. The lotus is viewed by Buddhists as a symbol of spiritual awakening. Confucius says of the lotus: “I have a love for the Lotus, while growing in mud it still remains unstained.” Hindus describe how Vishnu is awakened from the deep slumber of Mahapralaya by the cosmic vibration OM emanating forth from the void. As he awakens a lotus flower blossoms from his navel whereupon is seated Brahma who, at the command of Vishnu, creates the Universe. The lotus was also sacred to the ancient Egyptians who associated it with the sun, and hence with creation. All of these meanings, conveyed by and associated with these symbols, should be deeply contemplated. Sacred Geometry, it must be remembered, includes the dimension of symbolical meaning in its definition, for geometry pervades all of creation and serves as the most effective alphabet for the expression of the ancient divine language of the Gods in their communications with mankind.

In the book The Wonder Beyond, by artist and mystic Mayananda, the author presents an image of the rose and the lily adjacent to each other in such a way that the position of their petals reproduces Durer’s drawing of the unification of hexagon and pentagon by means of the Vesica.

Toggle back and forth between this page and the next to see Dürer’s geometry superimposed upon Mayananda’s alchemical drawing.

The banner reads “Igni Natura Renovatur Integra” a powerful alchemical formula in Latin that roughly translates as: “Through fire, Nature is entirely renewed” a formula that both conceals and reveals one of the great Hermetic secrets, that of the cosmic fire which periodically incinerates the world, sweeping away the old to make way for the renovated world. Remember, Adam was told to replenish the Earth.

The initial letters of the phrase – I. N. R. I. – yields an acronym that also stands for the Greek phrase Iesous Nazarenos Rex Iudorum, which translates as Jesus, the Nazarene, King of the Jews, the words inscribed by Pilate on the wooden sign hung upon the cross at the crucifixion. The significance of this unfolding juxtaposition of meanings, which was understood by Kabbalists, Alchemists, Freemasons and occultists of old, cannot be overstated.

It must be understood that the Crucifixion is a symbolical representation of a cosmic process, by which life is continuously sacrificed and renewed in order to achieve a higher state of existence. Jesus hung upon the cross as a symbolical surrogate for all mankind, as were all the divine saviors throughout time that were offered up in sacrifice to the redemption of the Earth and the life evolving upon its surface. In Sacred Geometry the cross is a symbol of the world of matter. When placed within a circle it is a symbol of the Earth itself. Jesus nailed to the cross of wood represents humankind crucified upon the cross of terrestrial, material existence, and it also indicates the means of effecting the return journey to our cosmic origins. For the cross in its static form is, geometrically, simply two perpendicular lines, a stationary symbol. But with the weight of the suffering born by mankind in fulfilling the mandates of cosmic destiny, the transverse arm of the cross is bent into a great arc, the cross becomes, in effect, a crossbow. The greater the weight of suffering the more powerful is the tension drawing back the great bow, the static has become dynamic, and like the vaults of the mighty cathedrals, is set to launch terrestrial Life, and the souls of Mankind, into the Great Deep of Cosmic Existence from whence we came.

On the second Tarot card of the Major Arcana The Magician is shown surrounded by roses and lilies, invoking all of the ideas associated with the symbolism of these two flowers. The Magician holds aloft his wand of power, representing the uniting of the forces of heaven with the forces of the Earth resulting in the fecundity and fertility symbolized by the abundant growth of the sacred flowers.

On the table are the four magical weapons – the Cup, the Sword, the Wand and the Pantacle, representing the chief tools of the Great Work and the 4 cosmic elements, which, when properly combined in the correct proportions, bring about the prolific evolution and transformation of both nature and the magician himself.

To the Egyptians the threefold petal arrangement of the lily, or its counterpart, the Lotus, symbolized Osiris, Isis and Horus, while in Masonic traditions they represented the three virtues of Faith, Hope and Charity. This trinitarian form of the petal array of the lily was symbolized in France and Byzantium by the Fleur-de-lis. (in French, fleur means flower and lis means lily.)

In the Middle Ages the symbols of lily and fleur-de-lis were confluent and could be associated with either Jesus or Mary. Both the lily and the fleur-de-lis were viewed as symbolical of the Holy Trinity.

According to some traditions an apparition of the Virgin Mary gave lilies to Clovis, the first king of the Franks, when, at the age of fifteen, he succeeded his father, Childeric as king in the year 481 A.D. Childeric was the founder of the Merovingian dynasty which ruled most of western Europe for 300 years following his rise to power. His son Clovis completed the task of consolidating the Frankish tribes into a single kingdom. A wealth of very powerful sacred history is woven about the succession of Merovingian kings, not the least of which is the idea that they may have been descended from Jesus, along with the tradition that they were guardians of the Holy Grail. This idea of direct descent from Jesus represents one of the most controversial propositions of recent scholarship. It forms the basis for the work Holy Blood, Holy Grail by Baigent, Lincoln and Lee, the Bloodline of the Holy Grail by Lawrence Gardner and other works. The Merovingians were succeeded, in the year 751 A.D, by the Carolingian dynasty, which takes its name from the family of Charles Martel and ultimately culminates in the reign of Charlemagne. The bee was a sacred symbol to the Merovingians, with some scholars suggesting that the bee was a precursor of the fluer-de-lis.

Transition from bee image to fleur-de-lis When the grave of Childeric I was discovered and opened in 1653 he was found to be wearing a cloak with 300 golden bees attached. In the year 1804 Napoleon had Childeriic’s golden bees attached to his coronation robe, which he justified on the basis that he was descended from the Merovingian line through the house of Stuart. It should be mentioned that buried along with Childeric and his bee adorned cloak was a golden bull’s head. The significance of this association of golden bees and bulls can only be appreciated through a deep reflection upon the hints conveyed through the Sacred Language, the Language of the Birds, that is, the language of the Gods, which reveals occult insight through tracing the evolving meaning of the words of our secular language back to their sacred origins.

By one of those odd coincidences that seem to appear so frequently throughout sacred history, Clovis gave his name to a prehistoric Ice Age culture in the Americas that existed at least 15 or 20 thousand years ago. The remains of this Paleolithic culture were first discovered near the town of Clovis, New Mexico. The town was named after that first Frankish king by the daughter of the local station master who, in the early 20th century, was immersed in studies of this intriguing and momentous period in European history which spanned the time from the rise of Christendom, through the decline and fall of the Roman Empire up to the onset of the Dark Ages. The evidence now suggests that the Paleo-Indian Clovis culture of North America largely disappeared in a series of terminal Ice Age catastrophes between 13,000 and 11,600 years ago along with dozens of species of Ice Age megafauna. While the first finds of the distinctive artifacts that identify the Clovis culture were found in New Mexico, the same toolkit has been found all over the contiguous United States, testifying to the widespread distribution of this ancient, lost society. In fact, the reach of this cultural phenomenon known as the Clovis appears to extend much further, even into to heart of Europe. Many similarities exist between the Clovis people of North America and the contemporaneous Solutrean culture of Northwestern Europe, whose geographic range extended throughout most of the domain ruled by Clovis and the Merovingian kings many thousands of years later. In other words, King Clovis gave his name to a town in New Mexico, which gave its name to a lost culture who were first discovered by their artifacts left behind near the town of Clovis, thereby inheriting the name of the town, and then subsequent discoveries demonstrate that the same Clovis culture of 15 thousand years ago evidently also existed in Europe in the very region ruled by Clovis and the Merovingians more than a dozen millennia later.

Regarding the Merovingians, the late Lawrence Gardner, author of Bloodline of the Holy Grail, wrote:

“The Merovingian kings were noted sorcerers in the manner of the Samaritan Magi, and they firmly believed in the hidden powers of the honeycomb. Because a honeycomb is naturally made up of hexagonal prisms, it was considered by philosophers to be the manifestation of divine harmony in nature. Its construction was associated with insight and wisdom – as detailed in Proverbs 24 : 13 – 14: ‘My son, eat thou honey, because it is good… So shall the knowledge of wisdom be unto thy soul..”

Nature’s choice of a hexagonal structure for the beehive is based upon he fact that the hexagon is the most economical shape in terms of expenditure of energy and matter in its construction in proportion to its overall strength. A beehive can hold up to 40 times its own weight in stored honey. This strength to weight ratio of the beehive has critically important significance in understanding the meaning of the bee and beehives in the ancient occult language of symbolism reaching from ancient Egypt, through the Merovingian dynasty, the medieval alchemists and Sufi orders and finally into modern Freemasonry.

Masonic Apron, 18th century, note beehive

From the mortuary temple of Queen Hatsheput, ca 1400 BC

Bees and the beehive carry the same meaning in Freemasonry as they did in ancient Egypt. Herein is concealed one of the truly great secrets of the ancient arcane traditions, for they symbolize the existence and identity of the Ones who, from time to time, reveal themselves to Mankind through the medium of celestial apparitions and visitations. This depth of symbolism will be explored in the intermediate and advanced classes now in preparation.

In occult symbology the number six and its geometric counterpart, the hexagon, are representative of the world and the cosmic domain. The pentagon represents the domain of life in a general sense and more specifically, the human domain. The association of the number 5 with humankind is overtly obvious with reference to the 5 senses, the 5 appendages, 5 fingers and so on. It is less obvious but no less a correlation between the number 5 and the domain of life that it appears in the 5 chemical classes of amino acids, the 5 nucleotide bases making up RNA and DNA molecules, the 5 carbon atoms in the deoxyribose sugar molecules of a DNA helical spine, and the 10 stacked nucleotide base pairs in each coil of the DNA helix. The generation of the linked hexagon and pentagon through the medium of the Vesica carries deep significance from the standpoint of Geometry. We see that the hexagon is the simpler of the two forms and occupies a preliminary position in the drawing exercise of linking hexagon and pentagon through the medium of the Vesica, necessarily appearing prior to the emergence of the pentagon, even as the cosmos had to exist before humankind could emerge out of the confluence of material and energy resources generated through the evolution of the universe. The hexagon, (world, cosmos) appears through a much simpler geometric process than the pentagon (life, humanity). The molecular architecture of biology utilizes the geometry of pentagons and hexagons and their interface in some very important ways. In the next bonus module we will delve deeper into the ramifications of the hexagon/pentagon link in the fundamental Sacred Geometry of Life.

Adenine molecule