I. General Symbolism of Shapes
It is generally held that all shapes have a definite psychological dynamic quality about them. Different shapes cause the human eye to move in different manners and to focus upon particular points, whether because of natural inclination or through social or cultural indoctrination. For instance, the eye will be naturally disinclined to focus upon any one point on the circumference of a circle, rather it will circumnavigate the shape continuously, rebuilding the mental image of a circle constantly. Likewise, the eye will traverse a quadrilateral shape in the direction in which it has been taught to read text. This is why artists sign their works in the bottom right corner, as this is the final place that the eye will fall upon (at least in the Western Cultures; Semitic people may observe a different dynamic).
As a rule, the properties of the dynamics of shapes are determined by either their ideographic qualities or by their mathematical properties, or by their symbolic association with a schema such as the Holy Qaballah.
Ideographic references of simple shapes
The most straightforward association that shapes have with concepts is their ideographic qualities. Entire Scripts and Alphabets are based upon this connection, as are a great number of non-linguistic signs (such as flowcharting symbols and road signs etc.). Viewed from this point, the most basic shapes can be said to have some very basic correspondences which are almost universally comprehended as such:
i. Circles are a symbol of wholeness, harmony or completeness (i.e. “to come full circle“). Symbolic of the Self as a unification of its separated Elements.
ii. Triangles are usually images of various trinitarian concepts: Salt, Sulphur and Mercury of Alchemy,; Father, Son and Holy Spirit etc. Also of Fire (as in Tejas or its Yetzirac Symbol) on account of its upward focus and flame shape in its upright forms.
iii. Squares tend to symbolize solid and stable concepts, often being associated with concepts of manifest form.
Qaballistic References of Shapes
The practical means of relating shapes to concepts or ideas is via some mathematically based schema or system of correspondences, such as the Holy Qaballah. For the purposes of Ceremonial Magick this is, of course, the most practical way to associate shapes with the broader practices of the discipline. Other systems exist which incorporate symbolic reference with various shapes, the Hexan system of symbols is a very excellent example of such schemas, for instance. Qaballistic correspondences are very similar to the Pythagorean theories upon shape, and the facts of Euclidean Geometry also bear heavily upon some of the Qaballistic attributions of various shapes.
i. Correspondences of some of the more simple lineal figures are as follows: Kether, the point; Chokmah, the line (or the circle); Binah, the triangle; Chesed, the square (or the tesseract), Geburah, the Pentagon or the pyramid (though this tends to be outside the parameters of our discussion); Tiphareth, the Hexagon or the Cube (but again this is outside of the discussion really); Netzach, the Heptagon; Hod, the Octagon; Yesod, the Enneagon and Malkuth has the Decagon and the Double Cube attributed to it (here though, the correct attribute of material solidity admits the possibility of the third dimension as the other Sephiroth could not before).
ii. Planetary Shapes are dictated by their Sephirotic correspondence. Saturn is attributed to Binah, three, and so to the Triangle (and to the Magick Square of three and so on); Jupiter is of Chesed, and thereby of Four and so the Square corresponds, but not the tesseract which is too abstract a shape to apply to the God of Law. The tesseract is more properly associated with the Watery quality of Chesed on account of its conceptual geometrical nature. Generally, all quadrilaterals (rectangles, parallelograms, rhombi etc.) all correspond to Chesed and to Jupiter if some law can be determined to render their shape regularly. Mars is of Geburah, the Fifth Sephirah, and so the Pentagon is correspondent (note that the Pentagon Building houses the U.S. Military administration). The Tetrahedron can be made to correspond here also but the non-material nature of the Sephiroth makes it difficult to employ this shape, except perhaps conceptually. Sol is attributed to Tiphareth and so to six, making its shape the Hexagon. The cube is not suited to the nature of Sol being a consummate symbol of the Element Earth. The Planet Venus is attributed to the seventh Sephirah, Netzach, and thereby to the Heptagon, which is also something of a symbol of the seven old planets and of the days of the week. Mercury is correspondent to Hod, the Eighth Light, and so to the Octagon, and Luna is attributed to Yesod, the ninth Sephirah, and so to the enneagon.
II. The Symbolic Correspondences of Various Lineal Figures
In addition to the basic geometric shapes that correspond to the Planets and the Sephiroth there is a large compendium of lineal figures that also express, sometimes very accurately, these same concepts in a more dynamic fashion. The interpretation of the symbolism of these figures is best determined by the manner in which they have been constructed and to a certain degree by the natures of the other similar figures with the same numerical properties.
Methods of Calculating Different Star Arrangements
Many of the geometric lineal figures, or stars, of the Planets (and thereby the Sephiroth; at least from Tiphareth to Malkuth) have more than one possible method of calculating the joining of the points. The lower numbers cannot be made into stars, as one and two points have no lineal figure, three is the triangle, without exception, and four has only the square or a shape that resembles two triangles joined by their single points, which can only be construed as a star by the longest stretch of one’s imagination.
The First “star” is of five points, called the Pentagram, and it is at once attributed to Mars, to the Elements and to the Microcosm, generally. There is only one way of connecting the five points to create a star, and often the direction of the line is indicated by the overlaps being exaggerated suggestively. The points are attributed to the Elements as follows: the top point (in the upright pentagram) is attributed to Spirit, the top left point to Air, the bottom left to Earth, the top right to Water and the bottom right point is attributed to Fire.
The Hexagram is generally attributed to the Planets, one per point with Sol at the centre. There are two methods of drawing a star with six points; firstly, two interlocking equilateral triangles, one upright, the other averse, making up the classical “Star of David”. The second method is the Unicursal Hexagram. The latter is a definite improvement upon the former as a symbol of the Solar force, implying its unity, rather than the duality implied by the Star of David. This is important as the Star of David is a symbol of the Covenant between Jehovah and his Chosen People. The Unicursal Hexagram shows the Solar force as being reflected materially via the Planets. The Points of the Hexagram are attributed to the Planets as follows: topmost point, to Saturn; top left point to Mars; top right to Jupiter. The bottom left point is Mercury; and the bottom right is Venus; the bottom point of the Hexagram is left then to Luna. The correspondences are drawn directly from the Tree of Life which is itself proportioned upon the relationship between the Pentagram and the Hexagram, being as it is a symbol of the Great Work (and very much else besides!).
The Heptangle has two possible permutations, one being attributed to the days of the week, and the other being the Holy Heptangle of BABALON. If one calculates the points by twos, the seven pointed star can be attributed to Our Lady and the interaction thus engendered by the lines indicate secret arcanums of the mystery of Babalon and the Beast upon which she rideth. The student should see The Vision and the Voice; A. Crowley; for a fuller explanation of this matter. Counting round the points by threes gives the Heptagon of the days, which when circumnavigated around it perimeter gives the Qaballistic order of the planets, whilst following the line of the star itself reveals the order of the days in the week. The Heptangle of Babalon is probably the most apt for use with the Planet Venus as there is an innate connection between these Goddesses. That is not to say that the other version is not applicable, and the individual must interpret his own situation and decide upon the configuration that best suits his current purpose. This is so for all of these polygrams, which can have a variety of implications depending upon which form is to be employed.
The octagon is another star with two possible forms based upon the odd or even progression between points. The octogram calculated on its’ even points is two interlocked squares though, and it is difficult not to allow their “square-ness” intrude upon one’s Mercurial intentions. The Octogram calculated upon its’ odd points though forms a regular pattern indicative of the mechanisms of the Great Work and of the Analysis of the L.V.X..
The enneagrams have three possible designs; calculated upon every second, third and fourth point. In the case of the enneagram of every third point, the star is composed of three interlocking equilateral triangles, which tends to express the Ideal Trinity in precise detail, that is as three interconnected triune conceptions in themselves. The two other enneagrams tend to indicate similar concepts. On the even points; the star is symbolic of the tendency in nature for forces to change into their opposites, subject into object and so forth. By fours this concept renders a star symbolic of the idea of constant change or motion upon an even more detailed or Elemental level. This last would tend to indicate a material lunar influence, whereas the enneagram of every second point is a more general lunar symbol. The more acutely angled star expressing a more sharply focused energy.
This process of interpretation can be extended indefinitely, though it is rarely necessary to go beyond the use of an eleven pointed star in most instances.
Some of the Symbolic Expressions of the Pentagram and Hexagram
The use of these lineal figures, the stars of the different Planets, is primarily as a form of expression of the magician’s particular objectives in some way. One may wish to imply the harmony and balance of the Planets as counterpoint to the central solar force, in order to place various aspects of oneself into their proper perspective. In this case, the Hexagram of interlocking Triangles may be employed as a figure drawn upon the temple floor. It is worth noting that each Triangle of this arrangement also corresponds to either Fire (upright) or Water (averse), and that the totals of the Planets of both triangles is equal (i.e. Saturn, Venus and Mercury = 3+ 7+ 8=18 and Jupiter, Mars and Luna = 4+ 5+ 9=18). There are doubtless several other hidden arcanums to be found in this simple symbol, and it is an important part of their numinousness that these qualities are discerned by the individual in the course of his own Great Work. In this way one will build up a large compendium of legible symbols for use in one’s magickal operations.
The intrinsic symbolism of the Pentagram is equally obvious to even a cursory study of the symbol. Each point being attributed to an Element can also be associated with a letter of Pentagrammaton, thus the Pentagram is a potent symbol of the formula of ALHIM [see Magick in Theory and Practice, Ch. IV; A. Crowley]. The progression of the points would then tend to indicate the particular combinations employed to invoke these various Elements, for instance the invoking pentagram of Fire begins at the topmost point of Spirit (v) and progresses to Fire (h), Air (t), Water (n), Earth (k) and finally returns to Spirit at the top. Symbolically then, the magician has called Spirit to manifest itself as Fire, in a defined space into which it is totally absorbed upon a material level, ending in the consciousness of the microcosm being elevated to a Spiritual Plane of Self awareness. There are four other formulae (as well as five reverse interpretations) attributed to the other points of this star, the Shield of Solomon that might be considered by the Neophyte before he uses the Pentagram rituals in his own temple.
Specialized Shapes and Lineal Figures
Apart from the Pentagram and Hexagram there are several shapes and Lineal figures that have certain symbolic qualities. Many of these are composites of two or more of the figures already discussed, as is the case with the Planetary Sigils for instance. In addition to the shapes outlined above, it is common to employ the crescent and the cross in the design of magical symbols of the Great Work. Less commonly, ovals, parabolas and hyperbolas are employed in a limited manner, and in the case of a variety of very specialized Sigils and so on, a number of very abstract combinations of curves and lines may create altogether unique shapes as a symbol of a very unique and well defined force [see Sigils of the Lemegeton].
In the case of the crescent, and to some extent the oval or egg shape, the attributions are largely ideographic, that is to say that they are really a stylized image of the concept that they represent. For instance, the crescent is commonly held to be a symbol of the Moon or Luna, and this is often thought to be on account of its similarity in shape to the last and first quarter phases of the moon as we view it from Earth. This is partially and superficially correct, but a closer examination of the natures of the Planetary symbols reveals that the crescent sigil of Luna connects the three Elements of Water, Air and Fire, making Luna to be something of a counterpoint to the gross manifest Earthly Element (itself a compound of Earthly qualities).
The Crescent is also a symbol of femininity and of the Element Water, partly because of its lunar association (although not of Yesod which is attributed to the complimentary Element of Air) and partly because of its shape being highly suggestive of a vessel capable of containing liquid, or of a flower (such as a lotus or crocus etc.) and so it is held to have feminine qualities.
The cross is by far a more complex symbol, deserving a more detailed inspection of its salient qualities. There are basically five kinds of crosses: Tau, X, Latin, Greek and Fylfot. From these, in combination and with other shapes, there are six more possible forms: Russian, Lorraine, Papal, Maltese, Crux Anastasia and Celtic.
Of the primary types of cross, the X shaped cross is very ambiguous, and tends to be more legible as a Rune (as in the case of ‘gyfu’ the Norse Rune meaning a gift) or a letter (as in X drawn perhaps from the Greek Sigma) and it is commonly a symbol of a kiss (i.e. xxx ooo at the bottom of a letter or a note).
The remaining four basic cross shapes have readily definable qualities that determine their symbolic correspondences. Taken singly then: the Tau cross is most commonly made up of ten squares and represents the ten Sephiroth, or the Great Work of uniting subject and object, macrocosm with microcosm (the proportions of this cross are 5 across the bar to 6 in height; with one “shared” square). As such the Tau cross is generally employed as part of the Magick Circle rather than in more specific enterprises.
The simplest form of the cross is probably the Greek cross, made of two lines of equal length, or of either five, nine or thirteen squares. In every case this type of cross symbolizes the Elements in harmonious balance, their centre being focused as the Element Spirit. This is absolutely so in the Greek Cross of five squares which has direct Elemental correspondence. The Greek Cross of Thirteen Squares represents these same Elements as their Astrological Signs centered around the spiritual Sun. The cross of nine squares tends to be slightly more obscure in its symbolic reference, again expressing through the ratio of eight circumferential squares to one central spiritual square, the mechanism of the Great Work. These eight squares represent polarized qualities of the Elements somewhat akin to the system of trigrams in the I Ching, and it is interesting to note the importance of both two and eight to the modern world of computing as being, in an abstract manner, also associated with this arcanum of symbolism.
The Latin Cross is slightly more complex in its symbolism than the Greek, its four arms held to represent the four Elements generally but often it is proportioned to correspond to the Sephiroth or the Zodiac, depending upon the intended application. Most simply it is composed of six squares and attributed generally to the five elements, the blank square having no well defined correlation. This is the basis of the Rose and Cross, around which an enormous arcanum of symbolism has been developed [see The Golden Dawn; I. Regardie]. Composed of ten squares it represents the Sephiroth but as an Expression of Tetragrammaton rather than the Triune Ideal of Kether-Chokmah-Binah. Made up of twelve squares it represents the gross and outward apprehension of the Elemental forces devoid of the spiritual-solar influence. This cross divides the Universe into its material components.
Finally, the Fylfot Cross, composed most basically of thirteen squares, represents the whirling force of the Universe, of constant motion. The device that it employs is partly ideographic (suggestively so) and partly by its association with the Signs being grouped Elementally around Sol so as to indicate something of a spiral progression (if the Signs are followed through the cross sequentially).
Of the compound crosses, most have very specific cultural symbolism. The most useful are the Maltese Cross which is a symbol of the four Elements in dynamic motion, the Crux Anastasia or the Ankh, which has a long history of its own as a symbol, and the Celtic Cross which is the essential form of the Rose Cross mentioned already. The Cross of Lorraine, Papal and Russian crosses tend to be compound forms of the Latin cross with slight variations on the same symbolic theme. In the case of the Russian Cross, the Fire and Earth arms are crossed by bars to indicate a manifested identification with god-head, the Tzars that employed this symbol were thus seen to be empowered divinely. So it is also for the Papal and Lorraine crosses which also express slightly different variations upon this theme. As such these crosses are of limited value to an individual’s Great Work in most cases anyway.
III. The Use of Polygons and Lineal Figures in Magick
Having determined the method of construction and the correspondence of the various shapes and figures, it remains only to consider how such potent symbols might best be put to task for the magician’s benefit. There are many arenas in which these symbols may be employed in a general sort of way, such as the decoration of the Temple, but for the purposes of depicting specific objectives, or attainments, there are three general areas of application. These three areas of use for symbol are all complex with a measure of variation even within their own domains, and often these areas of application overlap to a degree. These are: the construction of seals or signs, talismans, or of the Magick Circle, and each application requires careful consideration.
The construction of ‘seals’ or signs’ that express specific aspects of the individual’s Great Work.
Least commonly of the three applications of symbol in High Magick, is the creation of Seals or Signs of one’s Great Work. As one progresses in the Path, certain symbols may take on special significance to oneself. It may therefore be useful to adopt these symbols as a Sign of a certain attainment (such as taking a higher grade in an order, and so on). Complimentarily; one may design a seal or sign to indicate an attainment to which one is aspiring, such as the Rosy Cross Lamen of the Golden Dawn. Similarly, the seal of the O.T.O. for instance, combines the shapes of the vesica piscis with the solar triangle in a symbol that indicates that magical order’s aspirations.
The Beast 666, often employed dynamic symbols such as these to indicate his magick authority over the spiritual forces that he was commanding [see The Confessions of Aleister Crowley; John Symonds and Kenneth Grant]. Such was the Triangle of Horus that he employed whilst he belonged to the Hermetic Order of the Golden Dawn. In fact, it is this principal that forms the basis of all religious iconic symbolism whatever. Even major government and corporate organizations have been known to combine potent symbols in this manner to symbolize their objectives.
Related to seals and signs as such are the talismanic figures, and flashing tablets. A Talisman, for the purposes of this short discussion, is a symbolically shaped and decorated piece of card, metal or other similar media. Usually, magickal talismans are made from virgin card or stiff paper (310 gsm or heavier) as a sort of evolution from employing parchment or vellum, both difficult materials to manipulate. The use of modern materials in these constructions is discussed elsewhere more fully.
The particular application that shapes and figures have to talismans is twofold: the shape chosen for the talisman itself, i.e. Saturn’s talisman is triangular, Jupiter’s is a square, and Mars’ is a Pentagon and so on. More significantly; the use of these symbols applies to the inscription of the talisman, determining with mathematical accuracy the objective of the magician’s operation, and depicting legibly its’ attainment. This at least is the objective of talisman design.
For the Construction and Arrangement of the Magick Circle.
Finally, shapes and lineal figures are important in the construction of the Magick Circle, and that upon two levels. Firstly, and most obviously, the shapes and figures can be employed in the actual inscriptions of the Magick Circle (e.g. in chalk, upon the temple floor) and especially in the inscription of the Magick Triangle. Both of these potent weapons in the magician’s armory are, after all, shapes, no matter how fundamental they are to the practice of the High Arts. One may inscribe squares or pentagons upon the floor of the temple around the magick lanterns used to illuminate the Great Work, depending of course upon the appropriate correspondences. Even figures such as stars and crosses may be employed in this manner, thus fine tuning the general arrangement of the circle to better express the intent of the ceremony at hand.
More subtly though, and arguably more significant, is the use of these shapes and figures as a basis for a symbolic ritual gesture. For instance, during the performance of the Lesser Banishing Ritual of the Pentagram, the magician circumambulates once deosil, stopping at the cardinal points. This action implies two shapes immediately, the circle (obviously) and the square. Whilst the circle defines the consecrated space, the square makes the godhead materially manifest. The Qaballistic Cross, which begins and ends this Ritual, is another excellent example of a gesture employing a shape symbolically to imply its ritual intention. In this case, the operator is attempting to unite his elements into a spiritual focus. A close study of many traditional rituals will reveal similar qualities in them also. The Neophyte Ritual of the Golden Dawn is perhaps the most completely choreographed. Another obvious example is the Spiral Dance of the Wiccan practices.
It is easily understood how many men over the centuries have changed the world by the power of their symbols, and the manner in which they employed them to support their plans (e.g. Nazi Germany; Rome; the Ottoman Empire and so on). Corporations have well understood the sub-conscious forces that are motivated by shapes and colors. Even the greatest thinkers and scientists have really learned little more than the enlightened manipulation of various legible symbol systems, which are themselves compounded from these basic shapes and figures discussed already Scripts and numerals all have their genesis in ideographic representations of our world which are merely adaptations of these basic graphic design components rendered representatively and suggestively (for instance, the Hebrew letter Shin means “a tooth” and is shaped as a molar a, there are twenty-one other such glyphs in the Hebrew Alphabet. The Norse script or ‘Runes’ is similarly image based.
From the foregoing it can be seen that the study of Magick Art is a study of the nature and connotations of symbols and images generally. The greatest challenge for the Neophyte to this High Art of Ceremonial Magick is to build a legible, reliable and complete compendium of symbols for use in his own Great Work.
Addendum : The Use of Shapes and Figures in the Construction of the Magick Disk
-excerpt from The Magick Weapons
The design employed for the Magick Disk is of such importance as to merit a more detailed consideration by the Neophyte. The lineal figures used to make up the figures of the Pantacle are derived from the purest qaballah and they express the entirety of the Neophyte’s aspirations, being a consummate symbol of his Great Work. As this mandala is the symbol of the union of microcosm and macrocosm it forms the basis from which all other pantacles and talismans created for the operations of the magician will be derived. As has been touched on previously, the symbol of the microcosm is most commonly drawn from lineal figures related to qaballah and to Euclidean geometry. Thus, the basic images used are lines, circles, polygons and polygrams, and this is embellished by the use of various magickal sigils and inscriptions. These symbols represent the highest ideals, known by the adept, of himself and of godhead. Having already determined upon the circular shape of the weapon, it is then appropriate to determine the lineal figures which will compliment this shape whilst symbolizing the union of the macrocosm with the microcosm. In order to understand this fully it is expedient to determine the properties of the various shapes being considered.
The simplest figures after the circle, the triangles and the square tend to be employed in compound figures where their essential characters are expressed in a more manifest fashion. For instance, the equilateral triangle, when inverted upon itself, forms the Hexagram or ‘Star of David’, and implying the equilibrium of the Universe manifest as a union of opposites or of complimentary forces (see Newton’s Third Law of Motion). As such it is an excellent symbol of the essential solar force that is the foundation of all Earthly life. The square is a useful symbol of unity expressed as a quaternary ideal, such as the Elements or the Powers of the Sphinx. In combination with the circle it presented one of the most ancient philosophical pursuits, the squaring of the circle, much dwelt upon by the Pythagorean School of mystics. It represents the Word given abstract Form.
Most commonly the quadrilateral form is combined with the circle to express the Elemental nature of the magician’s unified Self, which is often represented by a circular arrangement of the Magickal Name of the Adept. The familiar correspondences of the Pentagram and the Hexagram need no explanation in this short essay, and used together they imply the Great Work in progress. The traditional interpretation of the inverted pentagram though can easily be reconsidered in a more realistic light. The sublimation of the Element of Spirit within the four manifest Elements calls to mind the method of the mystic, rather than the magician, and might be employed successfully to that end. Of course if one were to choose the discipline of Magick Art that is entirely black then the Pantacle of Leviathan would naturally be entirely appropriate for all of one’s workings. By making these kinds of uses of the familiar set of occult symbols it becomes relatively easy to design a Magick Disk that represents the individual magician perfectly adequately. By examining the other common lineal figures we can determine which, if any, may be appropriate to our own designs. The lineal figures of the Heptangle relate, in one instance, with the progression of the days of the week and the correspondence to the progression of the Planets upon the Tree of Life (see The Book of Thoth- Aleister Crowley). On the other hand, the heptangle formed by joining alternate points of the star is known as the Holy Heptangle or the Star of Babalon, and is a very potent symbol of the Great Work upon a larger scale (see The Revelations of St. John the Divine for references to Babalon and to the Beast upon which She rides). Unless these symbols relate directly to one’s Magnum Opus then it is probably not appropriate to employ these figures as they tend to indicate the goal of the Path rather than the traveler himself. Nonetheless, the innate potency of the symbolism renders the heptangles worthy of serious consideration. The octogram is an extension of four, one form of it is actually two interlocking squares, and therefore it is something of an extrapolation of the circle, and that circle is squared in a very intricate manner. The octogram, when calculated from its odd points (i.e. from every third point) implies the mechanisms of the Great Work, rather than its accomplishment. The enneagram is similarly an expression of the triangle, the simplest form being three interlocking equilateral triangles. Whilst a useful symbol of the discipline by which the Neophyte has bound himself to his Magnum Opus, the graphically unstable nature of these figures limits their appropriateness in the design of a Magick Disk to be employed by a magician who aspires to Adonai. Because of this though, Wiccan magi might find the symbolic geometry useful in their rites. One could be forgiven for assuming that the decagram is a suitable geometric shape for the design of this Pantacle, but close inspection reveals that it is something of a re-interpretation of the pentagram. Indeed, in one arrangement it is formed by two interlocking pentagrams, right and averse, again implying the dyadic nature inherent in the apprehension of Unity, but upon a base and illusory material level. If one were designing a Pantacle to attract material goods, this shape might be employed with good result, but the Great Work tends less toward material manifestation than to enlightenment, and the stagnant nature of these glyphs is a great limitation to their usefulness here.
Complimentary to this glyph is the eleven pointed star, which is a potent symbol of the Great Work in all of its forms. Essentially, this figure represents the union of the microcosm with the macrocosm as it is formed by the conjunction of the pentagram and the hexagram. Counting it by even points there are two circumnavigations of the circle bounding it, one of five points and the other of six. Counting in threes, it represents the triune manifestation of these basic principals as elemental energies, in fours the Elements are expressed as vehicles of the trinity such as Salt Sulphur & Mercury, Light, Life & Liberty etc. (see-Khabs am Pekht, Equinox Vol. III No. 1 – Aleister Crowley). Even so, the essential energies are best expressed by the star counting around every five points, which is also six points in reverse, and which in turn implies the Great Work directly as the expression 5=6:6=5. This lineal arrangement is in turn suggestive of the eleven pointed star of even points, with which it has a certain mathematical symmetry. Thus the eleven pointed stars tend to indicate the cyclical nature of the light which they graphically represent.