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We will now take another side-branch of the hexad to discuss the double hexad – or dodekad, that of twelveness.
The Dodekad – 12
The Dodekad is not included in the Decad (1-10); but relates intimately with each of them, even 7.
Twelve is double six.
It refines the Hexad’s structure-function-order and takes it to another level.
12 has 5 divisors (1, 2, 3, 4, 6).
12 is appointed at the archetypal level as the natural framework of arithmetic and geometry. It is found in the cube, octahedron, dodecahedron and icosahedron.
12 is the first abundant number.
This means its factors 1, 2, 3, 4 & 6 sum to more than itself.
1 + 2 + 3 + 4 + 6 = 16.
The Dodecagon – 1800°
Reference Construction Lesson #68: Constructing the Dodecagon.
The dodecagon is a twelve-sided figure.
Each outer angle = 150°. Each interior angle = 30°.
150 x 12 = 1800°
12 points on a circle can join to form 4 triangles, 3 squares, or 2 hexagons.
4 triangles in blue; 3 squares in green; 2 hexagons in red.
3 x 4 = 12
3 + 4 = 7
Sometimes 12 is associated with 7.
The 7 note musical scale (white keys on the piano) has the 8th as the octave.
The 12 note musical scale (white & black keys) has the 13th as the octave.
Credit: Michael Schneider
Michael Schneider writes, “When twelve such ‘moon circles’ are constructed within the band around the ‘circle of the earth’ as shown above, and a hexagram star is constructed within the bad, we see a more complete scheme rich in number relationships. For example, the combined radii of the earth and moon equal 5040 (= 1 x 2 x 3 x 4 x 5 x 6 x 7 = 7 x 8 x 9 x 10) miles, the number of the ‘ideal population’ of Plato’s utopian twelve-tribe nation of Magnesia described in his Laws. Plato disguised these numbers of the cosmic ideal throughout his writings to hint a the numerical and celestial scheme he wasn’t allowed to discuss overtly. The celestial design canon contained in the Delphic riddle of the squared circle served as the pattern for twelve-part temples, myths, measures, and societies throughout the world over many centuries.”
12 edges of the cube and octahedron
12 vertices of the icosahedron
12 faces of the dodecahedron
The 2nd most simple Pythagorean triangle is the 5:12:13.
12 spheres fit perfectly around 1 to define a cuboctahedron (vector equilibrium).
12 circles arrange around 1 to create the “Fruit of Life” from which Metatron’s cube and the Platonic solids emerge.
Twelve or Twelveness represents the “crystallized expression of divinity”.
Atomic Number 12 = Magnesium
Magnesium is the 8th most abundant element in the Earth’s crust and sixth most abundant metal. It is the 2nd most abundant metal in seawater, after sodium.
Magnesium is extremely important for life. It is the 2nd most important intracellular cation and is involved in a variety of metabolic processes including glucose metabolism, ion channel translocation, stimulus-contraction coupling, stimulus secretion coupling, and peptide hormone receptor signal transduction. In all it is needed for over 300 biochemical reactions.
It is used for medicinal purposes including milk of magnesia and Epsom salts.
Magnesium is important for plants as well as humans. At the center of every chlorophyll molecule there is a magnesium ion.
Credit: Robert Lawlor
Magnesium produces a brilliant white light when it burns in air. The metal reacts with water to produce hydrogen gas.
12: Base Precessional Number & Platonic Solids
12 is the base precessional number.
12 constellations in the zodiac or ‘ages’ of the Precession
12 edges of the cube and octahedron
12 vertices of the icosahedron & cuboctahedron
12 faces of the dodecahedron & rhombic dodecahedron
12 hours on a clock face (12 x 2 hours in a day)
12 x 6 = 72
72 is the preeminent precessional number.
The Sun moves through 1 degree of Precession every 72 years. That means 72 years = 1 “day” of Precession.
The sum of the angles of every single Platonic solid, Archimedean solid and Catalan solid are all factors of 72.
- 72 degrees F – considered ‘room temperature’
- 72 bpm = average human resting heartbeat
- 72 = The exterior angles of a regular pentagon
- 720 = sum of the angles of a tetrahedron
- 720 = sum of angles of a hexagon
- 720 x 2 = 1440 = sum of angles in a regular decagon, octahedron, and star tetrahedron
- 720 x 5 = 3600 = sum of angles in an icosahedron, cuboctahedron, truncated tetrahedron
- 720 x 6 = 4320 = sum of angles in a tetrakis hexahedron and triakis octahedron
- 720 x 9 = 6480 = sum of the angles of a dodecahedron; sum of angles of triangle to decagon
- 720 x 11 = 7920 = Diameter of the Earth in miles
- 720 x 12 = 8640
- 8640 x 10 = 86400 = number of seconds in a day
- 8640 x 100 = 864000 = diameter of the Sun in miles
- 720 x 14 = 10080 = sum of angles of icosidodecahedron
- 720 x 15 = 10800 = sum of angles in a pentakis dodecahedron, triakis icosahedron, and rhombic triacontahedron.
- 720 x 18 = 12960 = sum of angles in a pentagonal icositetrahedron
- 720 x 20 = 14400 = sum of all five Platonic solids
- 720 x 23 = 16560 = sum of angles in a truncated cuboctahedron
- 720 x 29 = 20880 = sum of the angles of 4 individual Archimedean solids: (rhombicosidodecahedron, snub dodecahedron, truncated icosahedron, truncated dodecahedron)
- 720 x 45 = 32400 = sum of angles in a pentagonal hexecontahedron.
- 720 x 59 = 42480 = sum of angles in a truncated icosidodecahedron
- 720 x 210 = 151200 = sum of all 13 Catalan solids
- 720 x 230 = 165600 = sum of all 13 Archimedean solids
It should be clear by now that the structure of cosmic space and the structure of time are all based upon the Platonic, Archimedean and Catalan solids. This is because the planets, solar bodies and galaxies literally move through these geometries. The geometry is an invisible Aether standing wave flow field in space created by interference patterns that physical matter coalesces upon.
Structure-Function-Order of 12
Proportions of everyday weights and measures based on the natural twelveness is evident in mathematics, which makes subdivision and multiples easier since 12 & 60 have so many divisors.
All 2D & 3D geometry is derived from base-60 mathematics – that of the 360 degree circle.
Base 12-60 math came from ancient Mesopotamia and the Sumerian culture (c. 4500 – 1900 BC). This is called the sexagesimal (base-60) numeral system. It is still used today for measuring time, angles, and geographic coordinates.
The number 60 is used since it is a superior highly composite number with 12 factors:
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
- 12 inches = 1 foot
- 12 x 3 = 36 inches = 1 yard
- 12 x 6 = 72 inches = 6 feet = 1 fathom
- 12 x 55 = 660 feet = 1 furlong
- 360 degrees = measure of a circle
- 60 minutes = 1 degree of arc
- 60 seconds = 1 minute of arc
Function (Weights & Measures)
- 12 = 1 dozen
- 12 dozen = 1 gross
- 12 ounces = 1 pound (original measure; now 16 oz = 1 lb)
- 60 seconds = 1 minute
- 60 minutes = 1 hour
- 24 hours = 1 day
- 30 days = 1 month (archetypal month)
- 12 months = 1 year
- 360 (+ 5) days = 1 year (360 days = the archetypal year)
“In ancient cultures timekeeping meant more than calculating festival dates and hours for prayer. It was a way that humans could see themselves integrated within the cosmic scheme. They accomplished this by making the basic unit of measure equal to the duration of one human breath (= 4 seconds.)”1
The ancient Hindu System of Time Measure
1 prana (breath) = 4 seconds
6 prana = one vinadi = 24 seconds
60 prana = 10 vinadi = 240 seconds = 4 minutes = time necessary for earth to rotate 1 degree on its axis
60 vinadi = one nadi = 360 breaths = 1440 seconds = 24 minutes = time necessary for earth to rotate 10 degrees
60 nadi = one sidereal day/night = 21,600 breaths = 86,400 seconds = 1440 minutes = 24 hours = time necessary for earth to rotate 360 degrees
“The people of ancient cultures saw themselves and their culture breathing in unison with the turning earth and stars.”2
86,400 = 12 x 12 x 660 = the number of seconds in a day.
The number of seconds in one day is 1/10th the diameter of the sun:
864,000 = 12 x 12 x 6000: the diameter of the Sun in miles.
21,600 = 6 x 6 x 60 = the number of breaths in a day.
The number of breaths in a day is 10x the moon’s diameter of 2,160 miles.
The Sun travels 21,600 mph through the galaxy.
There are 216,000 (60 x 60 x 60) miles between the earth and moon (mean distance).
2,160 = the length of each Zodiacal age in the Precession of the Equinoxes (1 Great Month)
25,920 (6 x 12 x 360) years = 1 Precession of the Equinox (1 Great Year)
25,920 miles = the circumference of the earth from Tropic of Cancer to Tropic of Capricorn.
The circumference is in resonance with the time of a precession.
“These number correspondences are not coincidental but recur wherever the cosmos is perceived as an integrated whole. The ancient duodecimal units of measure were carefully chosen and coordinated by seers to integrate human structure-function-order as distance-breath-duration with celestial rhythms and dimensions.”3
There are 12 chemical steps in every spiraling turn of the DNA helix.
Credit: Dr. Mark White
There are 12 cranial nerves in the head.
As Michael Schneider wrote, “In an advanced stage of meditation the head’s twelve cranial nerves are energized to liberate the individual as an enlightened being, a solar conqueror, a ‘self-rolling wheel’, world savior, avatar, messiah of the age, like a central sphere surrounded by twelve others, symbolizing the twelve attributes or powers.”
We use a 12 person jury to decide matters of ‘justice’.
There are many 12 tribe nations.
“The philosopher-leaders envisioned that by mirroring the night sky on earth they were participating in the harmonies of the cosmic structure-function-order.”4
- 12 Tribes of Israel
- Native America – 12 tribes consisting of 12 clans
- Solon’s Athenian society
- Ancient Ireland – its center at Tara, the High King’s celestial court
- 12 districts in ancient China, Egypt, and Greece
- Ancient Egyptian society divided into 12 nomes, or provinces
- Chinese courts
- European courts
“The twelve-part national myth of twelve-tribe nations is a tale about both the visible sun and the spiritual light within ourselves.”
See John Michell and Christine Rhone’s book Twelve-Tribe Nations.
Religion, Myth, Legend, Folklore
12 shows up frequently in religion, myth, legend and folklore from the world over.
- 12 Houses of the Zodiac
- 12 disciples of Jesus
- 12 disciples of Buddha
- 12 retainers of Osiris
- 12 ordeals of Gilgamesh
- 12 labors of Hercules
- 12 sons of Biblical Jacob
- 12 petals in the Anahata (heart chakra)
- Vedic kings surrounded by 12 nobles
- Norse god Odin and his 12 counselors/12 sons
- Dalai Lama’s Round Council of 12 great Namshans
- King Arthur and his Round Table of 12 knights –He subdued 12 rebel princes; won 12 great battles
- 12 gods and goddesses presided over by Zeus (12 Olympians)
- 12 powers of Apollo – Greek sun god
- 12 ships sailed by Odysseus, commanded by 12 followers
- 12 rowers in the ship with Ra
- 12 stones chosen by Joshua
- 12 harvesters in the Egyptian field of Amenti
- 12 vultures appearing to Romulus indicating the exact site of Rome in Roman myth
- 12 bronze tablets in ancient Rome bearing Roman law
These twelves of religion and myth all “symbolize our innate faculties of spiritual intelligence, twelve grades of being, twelve stages of unfoldment. These twelve phases of transformation are twelve ways we seek identity with our Higher Self.”5
See Article 259 for more info on the Zodiac.
There are 12 houses of the Zodiac.
There are 12 Ages of the Zodiac in the Precession of the Equinoxes.
These are: Aries, Pisces, Aquarius, Capricorn, Sagittarius, Scorpio, Libra, Virgo, Leo, Cancer, Gemini, and Taurus.
As Michael Schneider says, “Each individual comprises all twelve aspects of the whole, and we will eventually find within ourselves the principles represented by the symbols.”
Aries – I seek my Higher Self.
Taurus – I seek my Higher Self through what I have.
Gemini – I seek my Higher Self through what I think.
Cancer – I seek my Higher Self through what I feel.
Leo – I seek my Higher Self through what I create.
Virgo – I seek my Higher Self through what I learn.
Libra – I seek my Higher Self through what I balance.
Scorpio – I seek my Higher Self through what I desire.
Sagittarius – I seek my Higher Self therefore I am.
Capricorn – I seek my Higher Self through what I use.
Aquarius – I seek my Higher Self through humanity.
Pisces – I seek my Higher self and I don’t seek my Higher Self.
Michael Schneider writes, “The zodiac described the inner constitution of humans, the structure-function-order of ourselves, mirroring that of the universe. According to the ancients, the archetypal principles revealed by arithmetic and geometry, represented by the zodiac, seen manifest in the designs of nature, technology, art, the clock and calendar, temple architecture, myths, measures, and whole societies have correspondences within each of us. The initiate was taught to see the world inside-out, to see 12-part wholes as our reflection.”
12 & 13
12 and 13 are inextricably related arithmetically and symbolically.
12 is solar. (12 x 2 = 24 hours in a day; 12 months in a year)
13 is lunar.
12 months of a solar year contain 13 lunations (moon cycles). There are 13 full moons a year.
12 points occur at the crossings of a hexagram around the 13th at the center.
Exactly 12 spheres pack around a 13th sphere.
If you connect their center points you get a cuboctahedron (vector equilibrium).
The vector equilibrium has 12 lines radiating from a central point.
If you remove the central sphere, the remaining 12 collapse slightly to create an icosahedron (seen below).
There are also 13 spheres in a 3D Fruit of Life, and 13 circles in a 2D Fruit of Life.
- Schneider, Michael, A Beginner’s Guide to Constructing the Universe, Harper Perennial, 1994
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