This document discusses the history and spiritual significance of geomancy, or sacred geometry. It argues that geometric shapes like the tetrahedron, cube, and other Platonic solids have encoded symbolic meanings relating to the origins of the universe and human consciousness. These shapes were used in ancient artifacts and rituals around the world to help people connect to cosmic forces and tap into a "divine memory." The document presents examples of how geometric forms are represented in traditions like Hinduism, Native American rituals, and meditative body postures, believing they can cultivate a "liminal consciousness" bridging the mind and body.

1. Revitalizing Geomancy
Romance with geometric consciousness is how I experience geomancy. 8 For thousands of
years, people in every part of the world have made hand-scale models of what I think of as
geometric "seeds" (Plato's five element-shapes and two related rhombic figures) using wood,
reeds, clay, metal, stone, string. I encourage everyone I know to do the same to see for
themselves how accessible geo-mantic knowledge is for humans who seek it. The knuckles of the
human hand create virtually all the proportional lengths necessary to make beautifully sym-
metrical forms.
From carved Neolithic "bolas" to contemporary Southeast Asian woven reed spheres, such
teaching devices encapsulate the sacred dimensions of the Universe and assist the maker or
user in extending awareness of Self into the infinite macrocosm and microcosm of creation.
Intimate knowledge of these forms and shapes is essential to grasping the deep personal
mythology of geometry, and helps the human to tap into the divine "memory" of connection.
I teach geometry (geo + metry) as an art/science of consciousness. The Greeks considered it a
divine art. Linguistically, the me in geometry is the me in metaphysics, the holy spirit in the
middle, the human measure. Metr is not only "measure," but "mother" and "matter" as well. I
suspect a connection to Mitra, the divine Vedic principle associated with order in the dark
universe.
Figure 4. Hand-held, precisely crafted geometric artifacts.

2. ( Above ) Three models based upon identical icosa-dodecahedral symmetry include (from left) a
contemporary model of a virus; a 3000-year-old bronze figure possibly associated with Hecate,
the "Triple Goddess" 9 ; and a reed healing sphere from Southeast Asia. ( Below ) Carved stones
from Neolithic Scotland (possibly bolas) accurately represent the five Platonic solids at least 1000
years before Plato.
Plato regarded geometry as the ultimate mnemonic (memory-aiding) device that organized
primeval chaos. In Timaeus, he describes how theDemiurge (whom he calls "the god")
"remembered" itself within Chora (the oldest Greek word for "place")-thereby initiating order in
creation. 10 Chora (which is also related linguistically to Greek words for "chorus," "dance
ground," and "the beating of a heart") is, then, almost certainly the vibrating, intelligent divine
feminine Receptacle. Before there was matter, Chora (whom he also calls the "Nurse of
Becoming") held the disorganized and undifferentiated aspects of shape (morphai -the perfect
geometric forms), power (dynameis-fire, earth, air, water, and aether), and
feeling (pathe). The Demiurge infuses Chora to materialize all that physically exists, at every
scale . . . in a near-but-never-perfect replication of the Mother. 11 As above, so below.
Plato taught that the universe was constantly in motion, its elements in a perpetually fluid state of
transmutation dancing and spinning into and away from connectivity. The dance ground was, of
course, the eternal and unchanging body of Chora. In the stillness of meditation, the luminous
spherical human 12 was the ground of the perfect cosmic dance. Plato seems to have believed
that geometric mnemonics could actually link an individual to the collective memory of the human
species-even to the memory of origination of human material being,autochthony, the "springing
from the soil." He saw the five perfect figures not just as symbolic memory-aiding devices, but as
geometric forms mathematically encoding and exemplifying real connections and the formulaic
process of structural evolution in the material world.
The tetrahedron, for example, actually was (for Plato) the element of fire, the color "red," and
"first" in a chain of Being. Astrophysicists who subscribe either to the Big Bang theory or to the
alternate theory see fire as being present or instrumental in a first act of creation, yet Plato's
thinking in this regard has often been dismissed as highly mythological and primitive. Translations
of his works have generally been made by philosophers untrained in three-dimensional geometry
and likely unable to recognize the sophisticated connective patterns of natural form and flow that
Plato describes. 13
The legacy of contemporary Western education is that geomantic consciousness is not a taken-
for-granted aspect of our worldview and therefore we do not recognize our intimate formal
connectivity to the three-dimensional universe in which we live. What we call "learning" is typically
accomplished quietly, without motion, in two-dimensional contexts-reading, computing, gaming,
or watching media. Body wisdom is rarely integrated into this existential cognitive scheme despite
the lip-service currently being paid to multiple intelligences. Thus, it isn't at all surprising that
geosophic knowledge encoded in ancient artifacts, artwork, and texts has so often been
overlooked. In many ways, we hold the unfortunate stereotype that a still body indicates a
developed mind-and an active body, a simple mind. It is a pernicious and largely invisible
ethnocentrism that denies legitimacy to the activity associated with many ancient and indigenous
rituals. We do not any more easily imagine knowledge being produced by Greek, Hindu, or
Egyptian scholars dancing, singing and doing yoga in their academies than we do tribal people
who "dance, sing, and make that outrageous art!" as they engage in their own form of rigorous,
concrete experimental research and philosophy.
Geometry is a formulaic method for the cultivation of a liminal consciousness that can bridge the
mind/body gap. Common body postures in both meditation and certain forms of dance 14 are
actually multi-layered geometric mnemonics. The basic seated meditative posture of yoga,
the siddhasana or "adept" position also known as "perfect posture," aligns to an etheric
tetrahedron (Figure 5). The base of the spine, head, and two knees approximate its four corners.

3. This is probably the most loved and most familiar representation of the Buddha. Red, the color
associated with the tetrahedron, is the color of the first (sacral) chakra at the base of the spine as
well as the color of initiation and beginnings (e.g. blood at birth, circumcision, and menstruation;
red ochre on a corpse as it passes to new life after death). First in the series of regular geometric
forms, the tetrahedron- as fire -destroys while simultaneously creating new beginnings.
In a different way, the tetrahedron is also recognized as a primary structural archetype by
science. A. G. Cairns-Smith (1985), a noted biologist, has made a very convincing case that the
first organisms came into being in a bed of tetrahedral clay crystals. Clay itself is inorganic, but it
holds geometric information necessary for the formation of Earth and its creations in much the
same way that musical information recorded on a CD holds music by giving material structure to
wave forms. He does not go so far as to declare the clay "intelligent," but argues in effect for co-
creation: the tetrahedral crystals provide exactly the memory structure-very nearly a genetic
code-that reproducing organisms needed to remember in order to achieve structural integrity.
Buckminster Fuller used the tetrahedron as the foundation figure in all his design strategies and
argued that it was the most energy-efficient figure in nature.

4. Figure 5. In yogic "perfect posture" or "adept position," the body aligns with the tetrahedron.
The geometric character of written Sanskrit enhances the total semantic experience of Hindu
texts, which contain some of the most ancient, elegant and subtle geometric mnemonics. Again,
the red/fire/tetrahedron is primary. In the Beginning, states the Bhagavad-Gita, this world was
Self alone, in the shape of a person (Purusha). The name Purusha roughly translates as the
purifying burning (ush) that existed before the current material Creation (pur). One of the most
beloved two-dimensional images of Purusha can be easily envisioned as a tetrahedron within a
cube. (See Figure 6, keeping in mind that each face of a cube is a square.) Purusha experiences
loneliness and wishes a second Self into existence. Very roughly paraphrasing here: he was so
large as man and wife together, he made his Self fall in two, and thence arose husband and wife.
He embraced her, and men were born. This union of Purusha and Prakriti (the female half

5. generated from himself) is the deepest, most holy Hindu symbol of Creator and Creation. 15 The
divine coupling is inherently geometric in a very important way. Two (and only two) tetrahedra
"nest" in a cube-the yellow element of earth (created matter), second in the Platonic series.
A very similar visual metaphor is employed in Navajo ceremonies that bring to ritual life a
character named Yebitsai-"Talking God," also sometimes called "Grandfather God of the East,
the Dawn"-who guides and monitors. The numinous talisman used in his ceremony is a bundle of
four sticks, loosely fastened to each other end to end. Only Yebitsai's hands, which represent the
white dawn (the white octahedron of air, third in the geometric series) are ever seen; they
protrude through small holes in a black cloth which hides a magician who shape-shifts the sticks
into a tetrahedron, a square, various diamond-like perspectives of cube faces, and an edge.
Figure 6. The image of Purusha (center) as Vastu Purusha (in "demon" form, trapped by the gods
in a net) is used as a pattern for architectural layouts. It can be visualized as a tetrahedron (left)
. Prakriti and Purusha merge in the second stage of materialization; this union is represented
here (right) as two interpenetrating tetrahedra whose eight combined corners define the second
dynamic element of Plato's series, the cube.
Semantic Tracings
In the same spirit as the above, I experience semantics as the romance of semiotics . The
etymology of the word geometry is just one avenue into what appears to me to be a virtually

6. worldwide semantic core. Greek mythology, for example, preserves it as the matrilineage
of Chora-Gaia/Ge, Mnemosyne, and the Muses. Mnemonic derives from an old Indo-European
root sound men- that refers to qualities and states of mind and thought. 16 In Old English, the
connection between mother Gaia and her daughter Mnemosyne was preserved in the
word gemynd,"memory." The geomantic sound/meanings of ge, ga, me, and metr that create the
word "geometry" are neither uniquely Greek nor even Indo-European-but seem almost to be a
panhuman hymn of praise to Chora that has echoed around the world from primal sources.
Ge and Gaia are name/sounds of Earth gods and goddesses in countless mythologies. 17
Gender is almost irrelevant. There is Geb in Egypt ; Geb in Papua New Guinea among the Dani;
and Ge in the Caribbean . The Gaelic word for Earth is gabhal. Ga-oh and Hahgwehdiyu are
Earth creators among the Iroquois. Apache mountain deities are gahe. Among the Pueblo tribes
of the American southwest, they arekachinas. The sounds ka and ga are frequently inter-
changed. Gaokerena is the tree of life in the Iranian cosmology. Galaxy is "milk of the Mother
Goddess."
In the Philippines, gaia is a model to imitate. Among the Hopi, gahopi is the "right way of living."
In India, Gautama received enlightenment inGaya, the holy city of purification in Bihar
Province. Ngai is the creator of Earth among the Maasai of Kenya. Nga is the sacred sound that
opens the throat in Tibetan meditation. Linguists such as Cavalli-Sforza (1991) and Sherveroskin
believe that ngai may have been one of the first human utterances, a sound echoing forward from
more than 200,000 years in the distant past . . . meaning "I," or possibly "I breathe."
Ganga is goddess of the Ganges, the river of eternal life. The ganas are servants of Shiva, Lord
of the Dance of transformation of earthly elements. In Spanish, the fire of transformation
is ganas -desire, the energy of creation. Ganeo'o is the Iroquois dance of thanks to the Creator.
Our words Genesis, gene, genuine, and indigenous all flow from this same primal container of
sound and meaning. To genuflect, to bend the knee as a sign of worship, is to become one with
sacred geometry. Genu is an ancient sound that meant "angle." In Greek, it became gon -the root
of polygon, a figure with many angles or corners.
The sounds me, ma, mr, and metr can be thought of as liminal and almost always associated with
edge/dichotomies of life and death-mortality, mother, measure. In ancient Egypt, at least three
separate glyphs were homonyms sounded as "mr:" (1) a plow, which symbolized love and
cultivation; (2) an owl, which symbolized death; and (3) a triangle, which symbolized geometry.
The nasal bilabial "m" requires only the parting of the lips to create the sound "ma," and so it is
not surprising that a baby's first cry for its mother's breast is ma. In Hebrew, 'em is
"mother"; 'ammah is either "mother" or a unit of measure. 18 In Hawaii, Maui brings
death. Maya is the mother of Buddha, and maia is the measure of illusion. Ma'at is the ancient
Egyptian Lawgiver goddess. The yoga position of ultimate awareness and surrender to Earth-
Mrtasana, "corpse pose"-is, when seen "from above," identical to the most beloved
representation of the Virgin Mary standing with her open arms outstretched.
As in the word geometry, ma/mr/metr is often combined with ge to sound a sacred name .
Aurgelmir is the first being in the Norse universe who emerged from the great cosmic
void, Ginnungagap. Mageogeo is a creator in the Tuamotus; magatama are sacred crystals of the
Shinto Earth spirit religion in Japan . Zoroaster, a contemporary of Pythagoras, taught
that Gayomart (also called Gaya Maretan) was the primal human, a luminous spherical being.
Also intertwined in this semantic scheme is one other persistent sound- ang or ank, from which
we derive angle. The hieroglyphic symbol for "life" in ancient Egypt was the ankh-a sandal strap.
The circular part of the strap went around the ankle, the primary angle by which humans walk.
Linguists believe that about six thousand years ago, throughout most of Europe and India, the
sounds ang and ank both meant "angle" in the sense of "bending, or turning on an axis" (Watkins
1969). The sound gel (as in angle) was related to ge, but was more specific. It implied "to form

7. into a ball," "bright and shining." Perhaps it anticipated either Ge or the luminous spherical
human. The sound an meant "aloft" and, oddly, "an old woman singing." Angh carried the
meaning of "tight, painfully constricted"-the vaginal opening at birth? Angwhi was "snake." El was
the bend in the arm (the elbow) or the bend in the lower leg (the knee), but it was also the elm
and the alder-extremely common cosmic creation trees. In Gaelic, the very oldest and most
important unit of measure was the ell. 19
Neither linguists nor etymologists currently recognize a link
between angle and angel, however. Angel is thought to be a sound that originally meant
"messenger," one borrowed by the Greeks from an unknown Oriental source. I believe that
messenger was Hermes/Mercury, who is so often associated with earth energies and measures.
What could be called the "angel of geometry"- Plato's etherically luminous sphere of
hoops/triangles, aloft, spiralling, singing memory-does not exist as a documented cluster of
sound/meanings. Yet I have experienced myself as this Receptacle of consciousness as I have
sought her name in non-Western sources that combine the sounds ang with ge/gaia (and the
related ka) in sacred creative contexts. 20
In the Qu-ran of Islam, for example, ankabut is a trickster spider who miraculously spins a huge
web over the entrance to a cave in which the Prophet hides from those who seek to kill him
(Surah 29 in The Holy Qu-ran). The Hopi Spider Woman is Koyangwuti. A Maori ( New Zealand )
female nature spirit is Kurangaituku. Eskimo shamans are angakut, and the primary Creator
is Anguta. Tangaroa is the primary Polynesian Creator. Among the Chinese, the Creator
is Panku or Pangu. The all-present creator for the Zulu of South Africa is uMvelinqangi. Yang is
the creative aspect of the Tao, and altjiranga is the aboriginal Australian name for the Creative
primordial. Ultimately, the ge/ga sound is the most ubiquitous. English retains it in god. In
Gaelic, gael means "love" and gae is "cage" (the Cosmic Receptacle?). Gae is also "jail" (the
entrapment of spirit in matter, perhaps). 21
Plato's Timaeus systematizes an entire system of geometry that was at least 1000 years old at
the time he wrote, and the Demiurge that organized the wildly vibrating aspects of Chaos was
known long before to the Hindus. Even the sounds in the name Bhagavad-Gita ("Song of the
Blessed One") carry precisely the meanings of geometry. Gita is from gei, "to sing". Bha is "to
shine," and bhag is "to share out good fortune." Bhagha is "elbow, a bending, an angle." The
early voice of humanity seems, to me, to be fundamentally geomantic-a creation song, a living
process of interlingual connection that is endless, turning and bending itself, in and out of
empirical linguistic science and the wisdom of mythology.
Geomantic Harmony
The idea that the world is held in Chora (the dance ground), and continually sung into existence,
is perhaps most beautifully expressed by Aboriginals in Australia who view themselves as the
part of Earth responsible for remembering and chanting all the songs of creation. People who
forget sacred connectivity, who do not sing the praises of the Creator, are in countless
mythologies destroyed by earth, air, fire or water-by catastrophes of elements out of control, out
of balance, out of tune. The contemporary science of cymatics (Jenny 2001) is built from exactly
this wisdom: particles of matter assume and maintain coherent shapes as a function of very
specific interference patterns, the shape effect of overlapping vibrations (harmonies). Physicists
actually describe all matter in this way. In the infinitely hot universe of plasma energy, matter
forms as a kind of supercool crust (or bubble wall) created by the "beats" of juxtaposed wave
forms (Prokopec et al. 1995). The miracle is the universality of a limited number of "natural
forms" (simulacra) that seem to pervade the "crust" at every scale. The human eye/brain/mind
seems designed to see simulacra and to find great meaning in them (Michell 1979).

8. Simulacra are images of people and things that can be seen in rocks, clouds, smoke . . . Their
"appearance" is sometimes so aesthetic-and timing so powerful- that it can be difficult to believe
they are natural flow forms. Simulacra are common neo-shamanic and religious phenomena
(witness the significance attached to a Madonna perceived in the rust of a screen door or burned
onto a tortilla) and are often cited as evidence of divine interference in the affairs of humans. I
think of this response as an example of a much larger panhuman phenomenon known as the Law
of Similars-the belief that things that look alike must share an important sympathetic resonance.
The principal power of a shaman or seer is, possibly, the ability to visualize simulacra in detail at
extraordinary ranges of scale. This expanded power of sight brings with it the awesome
responsibility of helping to keep alive (and sometimes even restoring) the shapes of cosmic
harmony. 22 And sacred vision is only one of the extraordinary burdens a shaman- who is most
certainly a geomancer-must take on .
The techniques used to generate such visions are clearly both scientific and meditative. They
vary from culture to culture, but there are some striking parallels. The Oneida questing tradition
of sitting small, standing tall is identical to the principle of magnifying clairvoyance described by
Patanjali in the Yoga Sutras, numbers 27 and 28. It was possible, he said, to make oneself
infinitely small such than an atom would appear large in comparison-or large enough to see the
whole Earth. A kind of magnifying clairvoyance can also occur in dreams. The Hebrew tradition of
prophetic dreaming, for example, produced a vision of the world tree startlingly similar to
ultrasound images of a human placenta and embryo. The German chemist F. A. Kekule credits a
geometric simulacrum in a dream of Oroboros (the almost unimaginably ancient image of cosmic
energy as a vortex/snake swallowing its own tail) as the inspiration for his hexagonal model of a
benzene ring molecule.
Cosmic trees, entwined snakes and hexagon/turtle images permeate the artwork, mythology, and
dream visions of people everywhere. Cultures as remote from one another in time and place as
the Hindu, Maya, Aboriginal Australian, and North American Plains Indian have all emphasized
these symbols in sacred geometric contexts. Metaphors of the snake/tree (which I understand as
the principle of spiralling) 23 and the turtle/hexagon (possibly representing the powerful and
efficient "packing" of divine energy as matter . . . think honeycomb!) are perhaps the deepest
totemic meanings in the human psyche as well as the most basic representations of geometric
connectivity.
The cosmic tree is present in virtually every creation mythology. It is the axis, the orienting
principle-the spine of Chora, the spinning divine feminine Receptacle. Any tree can be the cosmic
tree, for branches grow from a living tree in a DNA-like snake of life that spirals in a phi ratio
(1:1.618). 24 Trees have been used throughout time as a starting point for teaching the
immanence of geometry in the everyday world.
I believe that the turtle, whose carapace is covered with hexagons, has remained so sacred
throughout time because it represents a threshold through which a variety of shapes can connect
(see Figure 7). Like hexagonal pegs, all five of Plato's perfect figures-and two other regular
figures, the rhombic triacontahedron (with its 30 identical diamond faces) and the rhombic
dodecahedron (with 12 identical diamond faces)-can be positioned to meet at this threshold and
to enter into structural connection with each other. 25

9. Figure 7. The H exagonal D oor is another vision that spontaneously opened to me as I explored
geometric consciousness. At the center is the tetrahedron. From upper left clockwise are the

10. rhombic dodecahedron, rhombic triacontahedron, cube, dodecahedron, icosahedron, and
octahedron.
Turtles and trees have appeared almost universally to create a picture of the cosmos as a vast
whirlpool, a maelstrom-what Giorgio de Santillana and Hertha von Dechend (1969) have
characterized as "Hamlet's Mill." 26 The gyroscopic spiralling of Earth's axis of rotation-known
technically as precession -has been recorded in countless mythological explanations of
observable, incremental and repetitive changes in the location of the sun and planets at particular
times of the year against the background of "fixed stars." In many stories Earth is a turtle, and S
nake (the hoopsnake or Oroboros, for example) is the path traced in the sky by Earth's axial pole
(the cosmic tree or churn in the mill) over the period of 25,920 years it takes to complete a
precession circuit around the ecliptic north pole . Draco (a dragon-snake) is the Western
constellation that curls around the ecliptic north pole-which is located at the "heart of the dragon."
The Hindu god Vishnu represents the cosmic tree . He is also a combined snake/turtle avatar, the
axis of every perfect spinning sphere. The name Cuculcan , Maya ruler of the four directions and
the four elements, means "to move round and round;" and cuceb (from cucul) is the spiralling of
the great wheels of the Maya calendar of days. In Norse mythology, the cosmic spiral is a squirrel
named Ratatosk who runs up and down Yggdrasil, the cosmic tree, carrying messages between
gods and humans. Oddly, the Maya word cuceb means "squirrel," after the spiral path the animal
takes as it scampers up a tree (Kenton 1928). 27