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The most familiar modern use — the culmination of the slow adoption Scholem traced, not an ancient survival.
Sacred geometry · 6 points · two triangles
Hexagram
The hexagram — two interlocking equilateral triangles around a central hexagon — is among the simplest figures in geometry and among the most over-told in history. It is the Seal of Solomon, the Hindu shatkona, and the Jewish Star of David, but the historical record is not what most captions claim. Here is how the figure is built from a single circle, the √3 math behind it, what the great scholar of Jewish mysticism actually established about its age, and how to use the overlay to check two triangles truly lock.
- Points
- 6
- Symmetry
- Six-fold (D6)
- Origin culture
- Cross-cultural; Jewish from ~17th c.
- Difficulty
- Beginner
- Built from
- Two equilateral triangles
- Also known as
- Star of David, Seal of Solomon, shatkona
See the hexagram on five subjects
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Centre the hexagram on an emblem and the two triangles should land on the same circle. If one triangle is even slightly larger, the central hexagon skews — the overlay catches it before it is cast or printed.
What the overlay shows
The hexagram overlay draws two equal equilateral triangles inscribed in a single circle — one pointing up, one pointing down — plus the regular hexagon they form at the centre. The six tips are the star points; the hexagon is the shared core. Because both triangles sit on the same circle, the figure is fixed by one compass setting, with no measuring at all.
In Grid Maker Pro the hexagram can be shown as the plain six-pointed star, with the central hexagon emphasised, or extended into the hexagonal lattice that connects it to the Flower of Life. Line weight, colour, and the bounding circle are adjustable. Build the figure on a blank canvas, or lay it over an emblem, window, or yantra to verify the two triangles are genuinely equal.
The math, briefly
The hexagram is two equilateral triangles sharing a circle. With the six points on a circle of radius R, each sits 60° from the next:
6 points · two triangles at 60° · √3 ≈ 1.732 · star area = 2 × hexagon
Three properties follow:
- It is a compound, not a true star polygon. Written {6/2}, the hexagram does not trace in one continuous line — it is the compound of two separate triangles, a distinction Coxeter draws when classifying star figures.3
- The star is twice the hexagon. The six points are six small equilateral triangles, and the central hexagon is six more — so the whole star has exactly double the area of the hexagon at its core, a clean √3 relationship of the kind Matila Ghyka catalogued.5
- It is six-fold geometry. The hexagram shares its symmetry and √3 proportion with the hexagonal circle grid, the family of six-fold patterns surveyed by Peter Stevens.8
The overlay keeps both triangles equal and on the same circle for you. Open it in the live tool and toggle the central hexagon.
History — what is real and what is myth
What the record supports
A cross-cultural magical sign. Long before it meant any one thing, the six-pointed star was a general protective and decorative mark — the Seal of Solomon — used across Islamic, Jewish, and European magic, often interchangeably with the five-pointed star. Its appearance in Islamic ornament is documented in Keith Critchlow's analytical studies.4
An independent Hindu tradition. The same figure is the shatkona in Hindu and tantric symbolism — the union of Shiva and Shakti — arising on its own rather than by borrowing. As Miranda Lundy notes, a figure this simple recurs wherever people interlock two triangles.7
The Jewish symbol has a datable history. The great historian of Jewish mysticism, Gershom Scholem, traced how the hexagram became the Magen David (Shield of David): a slow medieval adoption, formal use by the Prague Jewish community from the 17th century, and only then a near-universal Jewish emblem carried into the Zionist movement and onto the flag of Israel in 1948.12
Claims that outrun the evidence
"The ancient shield of King David." Scholem found no evidence that the biblical King David used the hexagram, and the "Shield of David" name attaches to the symbol only much later. The figure is genuinely old as geometry; its identification with David is a later tradition, not a documented fact.1
"A uniquely Jewish symbol." The hexagram's Islamic, Hindu, and European uses are at least as old as its Jewish one. Treating it as the property of a single tradition erases the shatkona and the Seal of Solomon — and the plain reality of convergent geometry.7
"It encodes a secret cosmology." The "as above, so below" reading is a real and beautiful symbolic tradition, but it is meaning assigned to the figure, not information stored in the triangles. The geometry is the same whatever story is told over it.
When to use it (and when not)
| If you want to... | Use the hexagram | Don't use it for... | Difficulty |
|---|---|---|---|
| Set out an emblem or seal | Two equal triangles read as instantly balanced and legible | A mark that must avoid religious or national reading | Beginner |
| Build a yantra or mandala centre | The shatkona is a natural, balanced hub for radial design | Asymmetric, expressive compositions (use a free canvas) | Beginner |
| Teach equilateral-triangle construction | Two triangles in one circle is an ideal first lesson | Lessons on proportion and ratio (use the φ grid) | Beginner |
| Verify a tattoo or pendant is true | Overlay exposes any inequality between the triangles | Freehand organic motifs with no triangle grid | Beginner |
| Link six-fold motifs across a panel | The √3 hexagon ties it to the hexagonal circle grid | Five- or eight-fold patterns (use those overlays) | Intermediate |
Where the figure genuinely appears
Six settings where the hexagram is documented — with an honest note where the history needs care.
Seal of Solomon
As a talisman the hexagram crossed cultures freely, often swapped with the pentagram — the figure's oldest documented role.
Hindu shatkona
At the heart of yantras the up-and-down triangles mark the union of masculine and feminine — an independent tradition of the same shape.
Prague community emblem
Prague's Jewish community adopted the hexagram as a formal emblem — a key documented step toward its modern meaning.
Gothic and Islamic tracery
Six-pointed stars fill rose windows and tiled panels as pure ornament — the hexagram as decoration, no symbolism required.
Modern brand and tattoo
The clean six-fold mark recurs in logos and tattoos, frequently paired with the Merkaba — its three-dimensional cousin.
Common mistakes
1
Calling it the ancient shield of David
Captioning the hexagram as King David's personal symbol states a tradition as a fact. The geometry is old; the Davidic identification is medieval-to-modern, as Scholem documented.
Fix: describe it as the Magen David and note that its adoption as the Jewish emblem is early-modern, not biblical.
2
Confusing it with the Merkaba
The flat hexagram and the three-dimensional star tetrahedron share a silhouette but are different figures. Treating the 2D star as a 3D solid muddles both.
Fix: use the hexagram for flat work and switch to the Merkaba overlay when you need the tetrahedral form.
3
Unequal triangles
If the two triangles are different sizes the points stop matching and the central hexagon turns irregular — the classic tell of a hexagram drawn by eye.
Fix: inscribe both triangles in the same circle so they must share one radius.
4
Claiming one culture owns it
Presenting the figure as exclusively Jewish, or exclusively anything, ignores the shatkona, the Seal of Solomon, and centuries of plain ornament.
Fix: name the specific tradition you mean, and treat the shape itself as cross-cultural.
How different disciplines use it
For tattoo and jewellery artists
The hexagram is a frequent request, and the symmetry is unforgiving on skin and metal — a triangle even slightly off shows immediately. Drop the overlay on the placement or the casting model, centre it, and confirm both triangles share the circle before you commit. For pieces that pair it with the Merkaba, switch overlays to check the flat and three-dimensional versions line up.
For designers
The six-pointed star reads as balanced and resolved, but it carries strong religious and national associations — use it deliberately, not by default. As a construction layer it gives a clean radial framework: derive a mark from the triangle intersections, keep the hexagon as negative space, then strip the scaffolding. Be aware of the contexts where the symbol will be read as more than geometry.
For architects
Six-fold geometry suits screens, railings, and window tracery, where the hexagram tiles into a hexagonal field without gaps. As an analysis tool the overlay reveals the triangle grid behind a historic rose window; for new work it offers a disciplined, repeatable module that details cleanly in metal, stone, or glass.
For educators
Two triangles in one circle is an ideal early compass lesson, demonstrating equilateral construction, six-fold symmetry, and the √3 area relationship between star and hexagon. It is also a model case for teaching how symbols acquire meaning over time — comparing the geometry's age with the documented history of the Star of David is a lesson in evidence.
"That which is above is like that which is below."
The Emerald Tablet of Hermes, Hermetic tradition6
Frequently asked questions
What is a hexagram?
A hexagram is a six-pointed star formed by two interlocking equilateral triangles, one pointing up and one pointing down, leaving a regular hexagon at the centre. Geometrically it is a compound of two triangles, written {6/2}. It is built from a single circle with compass and straightedge.
Is the hexagram an ancient Jewish symbol?
Not as old as commonly believed. The historian Gershom Scholem showed that the hexagram became a specifically Jewish symbol — the Magen David, or Shield of David — only in the medieval and early-modern period, and as a near-universal Jewish emblem mainly from the 17th to 19th centuries. There is no evidence it was the personal shield of the biblical King David.
What is the difference between a hexagram and the Merkaba?
The hexagram is a two-dimensional figure: two flat triangles forming a six-pointed star. The Merkaba is a three-dimensional figure: two interpenetrating tetrahedra forming a star tetrahedron. The 2D shadow of the Merkaba looks like a hexagram, but they live in different geometric spaces.
What is the Seal of Solomon?
The Seal of Solomon is the same hexagram used as a protective and magical sign in Islamic, Jewish, and European traditions. In much medieval usage the six-pointed and five-pointed stars were used interchangeably as the seal; the hexagram's role as a talisman long predates its role as a national or religious emblem.
What is the shatkona in Hindu tradition?
The shatkona is the hexagram in Hindu and tantric symbolism, where the upward triangle represents Shiva (the masculine principle) and the downward triangle represents Shakti (the feminine). It appears at the centre of several yantras. It is an independent tradition, not a borrowing — another case of the same simple geometry arising on its own.
What does the upward and downward triangle mean?
The most common reading is the union of opposites — heaven and earth, fire and water, masculine and feminine — captured by the Hermetic maxim "as above, so below." This interpretation is widespread across traditions, but it is symbolic meaning layered onto the figure rather than a property of the geometry itself.
What is the math of the hexagram?
The hexagram is governed by √3, the proportion of the equilateral triangle and the hexagon. The whole star has exactly twice the area of the hexagon at its centre, and its six points are themselves small equilateral triangles. Six-fold symmetry and √3 connect it to the hexagonal circle grid of the Flower of Life.
How do I know a hexagram is drawn correctly?
Both triangles must be identical equilateral triangles inscribed in the same circle, and the six points must reach the circle equally. The central hexagon should be regular. Overlaying the true figure on a design exposes any inequality in the triangles immediately.
References
- Scholem, G. "The Star of David: History of a Symbol," in The Messianic Idea in Judaism. Schocken Books (1971), pp. 257–281.
- Scholem, G. Kabbalah. Keter Publishing House (1974). ISBN 0-87068-867-X.
- Coxeter, H.S.M. Regular Polytopes. 3rd ed. Dover (1973). ISBN 0-486-61480-8.
- Critchlow, K. Islamic Patterns: An Analytical and Cosmological Approach. Thames & Hudson (1976). ISBN 0-500-27071-6.
- Ghyka, M. The Geometry of Art and Life. Sheed & Ward (1946). Dover reprint (1977). ISBN 0-486-23542-4.
- The Emerald Tablet (Tabula Smaragdina), in Holmyard, E.J. Alchemy. Penguin Books (1957).
- Lundy, M. Sacred Geometry. Wooden Books / Walker & Co. (1998). ISBN 0-8027-1382-X.
- Stevens, P.S. Handbook of Regular Patterns: An Introduction to Symmetry in Two Dimensions. MIT Press (1981). ISBN 0-262-19188-3.
Other Sacred Geometry overlays
Notes from the studio · Three practitioners on the hexagram
Illustrative composites of how the tool gets used in practice — not quotes from named individuals.
On a fine-line wrist piece a triangle a hair too big is obvious forever. I drop the overlay on the stencil photo and only ink once both triangles share the circle.
I cast the shatkona for yantra pendants. The hexagon at the centre has to be regular or the setting won't sit — the construction grid is how I check the wax before I pour.
When we teach symbols I show the same star three ways — Seal of Solomon, shatkona, Magen David. One overlay, three histories. Students never forget that geometry and meaning are separate.
Open the hexagram overlay
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