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I will not go into all of the specific details of Sacred Geometry. Getting spoonfed information can lead to misinterpretation and I do not want to accidentally omit important details for the occult student. What I will do however is present a personal analysis of mathematical syncronicity within the mystical symbols of the Pentagram and Hexagrams of Magick.

Before we break this down, first a little refresher from high school geometry class.

In order for a triangle to be present, the three intersecting line segments must meet each other at three angles which add up to 180 degrees, and form simultaneously a closed three sided figure.   Equilateral triangles have three equal angles and sides. The inner angles are each equal to 60 degrees.  Isosoles triangles must have two angles (X and Y for example ) of equal value with the third angle being their difference in the equation:

180-(X+Y)=Third Angle in Degrees.

Now, interestingly enough, mathematically a straight line has an angle of 180 degrees.  It is necessary to determine what the outer angle is for a triangle's corner, which will come in use later. Pentagons must have a total value of 5 equal inner angles that add up to 540 degrees. By geometical analysis we find that each of the five inner angles of a pentagon is 108 degrees. Hexagons have a total value of 6 equal inner angles that add up to 720 degrees. Do you see a pattern yet with the numbers? Hint: Think about numerology/Gematria.

Next, we have to analyze the Pentagram.  It is a five pointed star consisting of an inner inverted pentagon with the tip pointing downwards. If you take all of the above into consideration, each outer triangle equals 180 degrees within.  This added to the total value of angles of the inverted pentagon (540) yields us a number of 1440. See below:

The Pentagram

So once you add everything up to achieve a single digit, you get the number 9.  Nine is associated with the Hebrew letter Teht ( T ), because in classic Hebrew letters are used for number placement. This is number 8 of the Major Arcana of the Tarot, which is the Strength Card, and consequently the 5th sign of the zodiac (starting from Aries in Spring) of Leo. The Pentagram is a 5-sided figure.

But wait, there's more.  This number could also add up to 90. Ninty is associated with the Hebrew letter Tzah-Dee ( Tz ) which is connected symbolically to the Star card of the Tarot. The number of the Star (or Stars) card is 17. (1 + 7 = 8...which is the number of the Strength card). Even if we were to say 900, it still wouldn't matter because in classic Hebrew 900 is written by using the "final form" of Tzah-Dee which is written when the letter falls at the end of a word.

The Pentagram symbolizes the four elements of Air, Fire, Water, and Earth, with the pentagon being the center of union, and the uppermost tip being associated with the Spirit element before it transmutes into its four individual parts. The Pentagram also represents the Sacred Geometry of the Human body, with the proportions set in accordance with the spreading of the 5 points. (Head for upper, arms for side triangles, and legs aligned with the lower set. Picture DaVinci's human model drawing). It was also the five wounds of Christ in some early Christian Sects.  Because the Pentagram in many neo-pagan traditions is associated with the Goddess archetype, I have used the feminine colours of blue for water and green for earth, especially since the pentagram is used to represent the element of earth as well.

Now, let us take a look at the Hexagram.  This mystical shape is on the surface, a hexagon with six equilateral triangles radiating around it.  To the creative artist, and consequently the learned occult student, it is actually the union of an upright equilateral triangle and an inverted equilateral triangle. Combining the 6 sets of 180 degree tips with the total count of 720 inside the hexagon yields 1800 degrees. See below:

The Hexagram

Again, we have a total of 9 appearing in the Gematria of this symbol. Now, if you have been paying attention, all of the angles and their totals mentioned add up to the number 9.  In mysticism, the Hexagram symbolizes divine union and perfection. It is the alchemical hermaphrodite of the inverted triangle of water joining with its opposite force of the triangle of fire. The feminine principle connecting to the masculine principle to create and synthesize a new perfect principle.   Just as above, I have used the colours of yellow for air and divinty, and the red background of elemental fire to demonstrate.  This symbol is used as the Star of David, one of the special seals of the Banishing Ritual of the Hexagram, an arrangement of the 7 main astrological bodies in Magick (each tip a planet and the center is the Sun), and the Merkabah outline. The figure can also be seen as the descent of divine force into the material realm and human awareness as it passes through the Tree of Life, and the ascension of the human being to godhood meeting half way, at the point of Tiphareth, where one is supposed to find their Higher Self.

By imposing the Pentagram (1440) over the Hexagram (1800) we get a specialized new figure (and if done properly the appearance of the Seal that should be visualized in the Southern Quadrangle of the Banishing Ritual of the Hexagram sphere of influence arrangement) which totals 3240 degrees. I present, the Omnigram:

The Omnigram

Staying true to form, the perfect union of opposites should create a finalized form of transmuted Spirit, which in turn reflects the Spirit force that originated the four elements it spawned. Thus the blue of water and the red of fire make violet, which in traditional Magick is the colour of Spirit. The mystical colour is associated with the meditation upon the letter Tzah-Dee. Nine, is in and of it self the perfect combination of 3's. Three aspects of the Goddess archetype, three aspects of the God archetype, and the collective trinity of Goddess+God=Divine Source. Within the Hexagon the pentagon of the Center principle forms four equal triangles that seem to point upward towards the heavens. Meditate upon this, and you will find much peace in regards to the beauty of Divine principle and thought.


Khalell Zen Paraldan, Frater Sacramentum Regis et Lucem (S:.R:.E:.L:., CLXVIII) W.W.B.D.

-written 1/8/05 at the House of Horus Temple (Bristol, Tennessee USA)

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