Showing posts with label Symbolism symbols. Show all posts
Showing posts with label Symbolism symbols. Show all posts

Thursday, 8 January 2026

The Septogram and the power of 7

 The Septogram: A Gateway to the Mystical Seven


In the shadowed realms of ancient wisdom, where geometry dances with the divine, there emerges a symbol of profound enchantment—the septogram, also known as the heptagram, the seven-pointed star. Unlike its more familiar cousin, the pentagram, which binds the earthly elements in five sharp points, the septogram weaves seven rays in an unbroken, continuous line, forming a star that pulses with the rhythm of eternity. Drawn in a single stroke without lifting the pen, it embodies infinity, a sacred loop that returns to its origin, whispering of cycles unending and mysteries veiled.


The number seven has long been a key to the cosmos. It echoes through creation itself: the seven days of genesis in ancient scriptures, the seven classical planets that once governed the heavens—Sun, Moon, Mercury, Venus, Mars, Jupiter, Saturn—the seven notes of the musical scale, the seven colors of the rainbow, and the seven chakras aligning the human spirit. In alchemy, the septogram evokes the seven metals and their transmutations, a ladder of ascension from base matter to celestial gold. In Kabbalistic traditions, it resonates with the sphere of Netzach, the realm of Venus, victory, and enduring love, a beacon of harmony amid the Tree of Life.



Yet the septogram’s true mysticism unfolds in its role as a bridge between worlds. Among modern pagans, witches, and those who heed the call of the Otherworld, it is revered as the Faery Star or Elven Star—a luminous portal to the realms of the Fae. Its seven points extend beyond the four cardinal directions and the upward reach of spirit (as in the pentagram) to include Below and Within: the hidden depths of the earth and the secret chambers of the soul. These points are often attuned to seven sacred qualities—magic, connection, inspiration, joy, trust, honour, and knowledge—or to the seven directions that encompass all existence.


To gaze upon the septogram is to feel the veil thin. It is said to be a gift from the faeries themselves, bestowed upon humanity to ease communion with their ethereal kin. Worn as an amulet, it wards against malice, much as it once served in older Christian lore to repel evil through the perfection of seven days of creation. In Thelemic rites, it crowns the Star of Babalon, embodying divine femininity and the ecstatic union of wills. For the seeker, it serves as a focus for meditation, drawing the mind into spirals of insight, where the mundane dissolves into the magical.



In its sharp, interlacing form—often the {7/3} variant, where lines connect every third point—the septogram reveals sacred geometry’s hidden order. It is no mere ornament but a talisman of power, inviting us to embrace the seventh mystery: the synthesis of all that is seen and unseen. In a world of fragmentation, it reminds us of wholeness, of the eternal dance where mortal and immortal entwine.

Behold the septogram, and let its light guide you through the mists.


The Septogram and the Rhythm of the Seven Days

In the veiled tapestry of mystical symbolism, the septogram (or heptagram)—the seven-pointed star—resonates deeply with the eternal cycle of time, particularly the seven days of the week. This connection arises not from mere coincidence, but from ancient astrology and sacred geometry, where the number seven binds the celestial to the terrestrial.


The seven points of the septogram correspond to the seven classical planets known to antiquity: Sun, Moon, Mercury, Venus, Mars, Jupiter, and Saturn. These “wandering stars” governed the heavens in ancient cosmology, and their influence birthed the very names of our weekdays.

•  Sunday — ruled by the Sun

•  Monday — ruled by the Moon

•  Tuesday — ruled by Mars (from Norse Tiw or Roman Mars)

•  Wednesday — ruled by Mercury (Norse Odin/Wodin)

•  Thursday — ruled by Jupiter (Norse Thor)

•  Friday — ruled by Venus (Norse Frigga/Freya)

•  Saturday — ruled by Saturn



The profound link manifests when these planets are arranged in a circle according to their perceived orbital speeds (slowest to fastest: Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon). Connecting them in the sequence of the planetary rulers of the days—starting from the Sun (Sunday) and proceeding to Moon, Mars, Mercury, Jupiter, Venus, Saturn—traces the lines of the {7/3} heptagram, one of the acute forms of the septogram.

This geometric revelation, preserved in occult traditions from Babylonian astrology through Hellenistic and medieval sources, illustrates how the septogram embodies the flow of time itself. Following its interlacing paths reveals the order of the days, a magical mnemonic for the cosmic rhythm that structures human life.


In Christian mysticism, the seven points evoke the seven days of Creation, a symbol of divine perfection and protection against chaos. In Kabbalah, it aligns with the sphere of Netzach (Venus) while encompassing all seven planetary influences. For modern pagans and those attuned to the Faery Star (another name for the septogram), the points may extend beyond planets to include directional or qualitative correspondences, yet the planetary-week association remains a foundational layer.


Thus, the septogram is no static emblem but a living mandala of temporal magic—a star that turns with the wheel of the week, reminding us that each day pulses with a unique celestial energy, guiding ritual, meditation, and the dance of existence.


Wednesday, 7 January 2026

The Five Pointed Star

 Exploring the Geometry of the Pentagram The Golden Star


In the elegant domain of star polygons, the be pentagram—denoted by the Schläfli symbol {5/2}—stands as a pinnacle of geometric harmony. This five-pointed star emerges from connecting every second vertex of a regular pentagon, or equivalently, five equally spaced points on a circumscribed circle. Unlike a simple pentagon {5/1}, which forms a convex hull, the {5/2} introduces self-intersection, creating a star with a density of 2, where lines cross to form a central pentagonal core.



It is come to represent several different forms including the commonly seen 5 elements pentagram, alchemical, chaos, the encircled pentacle, the Tetragrammaton, as well the inverted version that represents a second degree witch and the  3rd degree and Elder broom versions. The inverted pentagram also represents the Baphomet and Satanism in some circles.



Construction and Basic Form


To construct the {5/2} pentagram:

1.  Inscribe five points equidistantly on a circle (separated by 72° angles, as 360°/5 = 72°).

2.  Connect each point to the one two steps away (skipping one vertex). This yields a single, continuous line that traverses all points before closing, manifesting as a sharp, interlaced star. The result is chiral—its mirror image is {5/3}, which is equivalent to {5/2} traced in the opposite direction, as 3 ≡ -2 mod 5.


Geometrically, the pentagram divides the circle into arcs and creates internal intersections. Each side intersects two others, forming five intersection points that themselves outline a smaller inverted pentagon. This self-similar property allows for infinite recursion: within the core pentagon lies another pentagram, scaled by the golden ratio, ad infinitum.






Symmetry and Properties


•  Symmetry Group: The pentagram exhibits dihedral symmetry Dih₅ (or D₅), with 10 elements: 5 rotations (multiples of 72°) and 5 reflections across axes through vertices and midpoints.

•  Area and Metrics: For a pentagram with circumradius R, the area is (5/2) R² (√(25 + 10√5) - 5)/2, derived from decomposing into triangles. Its vertex angle is 36°, with internal angles at intersections of 36° as well.

•  Dual and Compounds: The pentagram is self-dual; its line arrangement is topologically identical to itself. It forms part of the pentagonal compound {5/2} ∪ {5/3}, known as the pentagrammic bipyramid in higher dimensions.

•  Topological Density: As a star polygon, its Euler characteristic is V - E + F = 5 - 10 + 1 = -4 (considering the star as a single face with windings), highlighting its non-convex nature.


Beyond pure geometry, the {5/2} pentagram whispers of cosmic order, symbolizing the five elements in ancient traditions or the human form in esoteric lore. Yet in its lines and ratios, it reveals mathematics’ timeless dance—a star where finite form echoes the infinite.