Free Islamic 12 Point Star Grid Generator
Construct the Islamic 12 point star instantly with our 100% free grid generator. Rotate two hexagons 30 degrees with the dodecagon through every midpoint, ready for tiling studies over any image, then export SVG or 600 DPI in seconds. No signup, no downloads needed. Trusted by 60,000+ artists worldwide.
Three squares, or four triangles
Twelve points on one circle, built by rotating a square through 30 degrees twice or by overlaying four triangles. Twelve-fold symmetry admits more tiling arrangements than eight, which is why it carries the more elaborate girih.
4 controls, not a fixed picture
Set size and construction step, toggle inner 12-gon and boundary circle. Every one is live on the canvas.
Stacks with sacred geometry & pattern
Overlays combine, each carrying its own transform, so this one can sit under or over flower of life, sri yantra and metatron’s cube, and 15 more in the same set.
Exact enough to repeat
Twelve-fold geometry is unforgiving of rounding; SVG export keeps the angles exact. Raster up to 600 DPI when printing rather than machining.
| Ctrl + Z | Undo |
| Ctrl + Y | Redo |
| Esc | Deselect overlay |
| Alt + drag | Free positioning (no snap) |
| Ctrl + scroll | Zoom canvas |
| Ctrl + P | |
| ? | Show this help |
The richest unit in Islamic geometric ornament, and one of the simplest to build: two hexagons on one circle, turned thirty degrees from each other, with no measurement anywhere in the construction.
The twelve-pointed star generator draws one of the 82 composition overlays in Grid Maker Pro, and the rest stack on the same image.
- 2 hexagons
- 12-gon at 0.866
- SVG + 600 DPI export
- Nothing uploaded
What is an Islamic twelve-pointed star?
The Islamic twelve-pointed star generator is a free browser tool that draws the twelve-fold star over any image or blank canvas. Two hexagons are inscribed in the same circle, one turned 30° from the other, and their overlap produces twelve identical points. The overlay also draws a dodecagon at r√3/2 — 0.86603 of the radius — the polygon whose vertices touch all twelve edge midpoints of the two hexagons. The boundary circle and the dodecagon can each be shown or hidden.
How to draw an Islamic twelve-pointed star
Two hexagons rotated against each other, the twelve-pointed star between them and the interior polygon they define. One tile of a much larger pattern.
Open the star
The Islamic 12 point star opens with both hexagons inscribed in the same circle and exactly 30° apart. Twelve points is enough that a small error in one hexagon reads immediately as a limp point next to a sharp one.
JPG · PNG · GIF · WEBP
Decide what the figure is for
The star alone is a mark. Add the dodecagon when you are building a pattern outward from it, and the boundary circle when the unit has to register against neighbours.
Size · Inner 12-gon · Boundary circle
Place it, then export
Drag, scale and rotate it over your artwork or work on a blank canvas at your paper size. Export SVG for a cutter, plotter or tile layout, or a raster at up to 600 DPI.
PNG · JPG · PDF · SVG · up to 600 DPI
Three steps, about a minute. No signup, no upload.
What the Islamic Twelve-Pointed Star Generator does
Twelve points, all identical
The Islamic 12 point star is two hexagons and nothing else. At twelve points the eye compares neighbours constantly, so a hexagon a degree out produces a run of points that are visibly not the same as the rest — far more obvious than the same error at six.
The dodecagon on the midpoints
It sits at r√3/2 and touches all twelve edge midpoints of the two hexagons. That is a construction line rather than the outline of the star's core, and the distinction matters when you are placing elements against it.
Twelve is the richest fold
Twelve-fold symmetry contains two-, three-, four- and six-fold inside it, which is why so much girih work is built on it — one unit can host square, triangular and hexagonal sub-patterns without any of them fighting the frame.
Every part separate
Hexagons, star, dodecagon and circle are independent toggles. A pierced version usually needs two of them; a repeating field needs the circle for registration; a finished mark usually needs only the star.
Over your own work
Its own transform, so the star can be rotated onto a photographed panel or scaled into a layout without disturbing what is underneath.
Vector out, at real size
SVG export gives true straight lines for cutting, inlay and tile setting. Raster export is sized from the paper format and DPI you choose, up to 600.
Islamic twelve-pointed star examples: four ways the figure reads
Islamic twelve-pointed star vs a downloaded star graphic vs compass and straightedge
| Option | Hexagons exactly 30° apart | Dodecagon on the edge midpoints | Vector export | Cost |
|---|---|---|---|---|
| Grid Maker Prothis tool | Yesby construction | Yesdrawn at r√3/2 | SVG + raster to 600 DPI | Free |
| A downloaded star graphic | Usually, unknown provenance | Rarely a separate path | Sometimes | Free or paid |
| Compass and straightedge | Yessix marks and a bisection | By construction | No | Time |
| A drawing program's polygon tool | Yes | Only if you build it | Yes | Subscription |
Who an Islamic twelve-pointed star is for: fields that have to carry more than one rhythm
How an Islamic twelve-pointed star works — Twelve from two hexagons, and why twelve is the fold the tradition prefers
If the eight-pointed star is the most common unit in Islamic ornament, the twelve-pointed one is the most capable of the 82 composition overlays that build from it. Here is the construction, the dodecagon that is not where you might expect, and the specific property that made twelve the fold so much of the tradition is built on.
Draw a circle. Step the compass around it at its own radius to get six marks, and join them into a hexagon. Bisect one of the arcs to find the halfway mark and step round again for the second hexagon, turned thirty degrees. The two overlap into twelve identical points.
As with the eight-pointed star generator, there is no measurement anywhere. Six marks come free from the radius, and halving an arc is a compass operation. That matters historically: a construction that needs no numbers can be transmitted by demonstration and executed on a wall by a craftsman with a cord and a nail.
Twelve is the fold that agrees with everything else. That is why the tradition kept coming back to it.
Where the dodecagon actually sits
The overlay draws it at r√3/2 — 0.86603 of the radius — with its vertices on the midpoints of the hexagons' edges. That is the classical construction polygon, because edge midpoints are findable with a compass before the star exists.
It is not the polygon where the two hexagons' edges cross, which sits slightly further out at 0.89658 and is the boundary of the star's solid core. The two are only about three percent apart, much closer than the equivalent pair in the eight-pointed star, which is why the distinction is rarely noticed here. It still matters if you are placing an inner motif: to sit in the star's core, work to 0.897; to sit on the construction, work to 0.866.
Why twelve rather than eight or ten
Twelve divides by two, three, four and six. A twelve-fold unit therefore contains square symmetry, triangular symmetry and hexagonal symmetry simultaneously, and a designer can develop any of them inside the same star without the sub-pattern disagreeing with the unit that contains it.
That is a genuinely unusual property. Ten-fold gives you five and two and nothing else useful; eight gives four and two. Twelve is the smallest number that carries the three tilings of the plane — square, triangular and hexagonal — inside one rotational symmetry, and that is the practical reason so much girih work is twelve-based rather than ten- or eight-based.
The twelve-pointed star overlay page works through the tilings, beside the rest of the sacred-geometry category. It also tiles well in company. A regular dodecagon cannot tile the plane alone, but it does so readily with squares and triangles — the semi-regular arrangements where dodecagons sit at the nodes and the gaps are filled with simpler shapes. That is exactly the structure of a great many historical star patterns, with the twelve-pointed star occupying the dodecagon's place.
Building a pattern from the unit
The usual method is to place the stars on a triangular lattice rather than a square one, so each star has six neighbours rather than four. Step the unit by one diameter along each of three directions at sixty degrees, and the gaps between neighbouring stars become the field where the secondary pattern is developed — the interlacing straps, the smaller rosettes, the filler shapes.
Use the boundary circle to register that. Twelve near-identical points are easy to misalign by one when you are stepping a unit by hand, and a repeat that is one point out is a repeat that has to be redone. A circle's centre and edge are unambiguous.
What is documented and what is not
That Islamic craftsmen built enormously sophisticated star patterns from compass-and-straightedge constructions is thoroughly documented — there are surviving pattern scrolls, notably the Topkapı scroll, that record the underlying construction lines rather than only the finished designs.
What is much more recent and much more contested is the claim that some late medieval Islamic tilings anticipate aperiodic tiling in the modern mathematical sense. There is a real academic argument there and it concerns a small number of specific decagonal patterns, not twelve-fold work in general. It is worth reading rather than repeating, and it is not a claim this figure supports.
Making things from it
For cut and inlay work, export SVG with the parts separated: the hexagons as construction, the star as the cut path, the dodecagon as the boundary if the centre is a different material. Twelve acute points are more fragile than eight, and a raster edge will round every one of them at any size a cutter or a kiln cares about.
For drawing, use the construction-step control and build it by hand once. Circle, six marks, first hexagon, bisect, second hexagon, star, dodecagon. Once the sequence is in your hands the overlay's job becomes checking a repeat rather than producing a unit, which is where it stays useful — accumulated error is invisible in one star and unmistakable across a panel of thirty.
Reading a historical example
Photographs of real panels are the best source and the worst thing to trace. Fit the overlay to the star instead — scale until the twelve points sit on the photographed ones — and the two hexagons show you the setting-out the maker used, including where it drifted.
On twelve-fold work that drift accumulates faster than on eight-fold, because there are twelve points to keep equal rather than eight and each one is a smaller angular slice. A panel that looks perfectly regular in a photograph will often show a degree of variation once an exact figure is laid over it, and knowing whether you want to reproduce that or correct it is a decision worth making deliberately.
The other thing the overlay reveals is the pattern's underlying grid. Once one star is fitted, stepping the overlay to the neighbouring stars tells you immediately whether the panel is set out on a triangular lattice or a square one — which is the single most useful thing to know before attempting a reproduction, and the thing that is hardest to judge from a photograph alone. The hexagonal grid generator tiles the lattice these hexagons come from, which is the ground the whole pattern sits on.
Where an Islamic twelve-pointed star gets used
Panels. Twelve gives me square and triangular sub-patterns in the same unit, which is the only reason a complex field holds together instead of arguing with itself.
I check repeats with it rather than draw units. One star is always fine; thirty stepped by hand is where the error shows, and that is what I need to catch before firing.
It follows the eight-pointed star in the lesson. Same method, one more bisection, and students see that the whole tradition is two moves repeated.
Islamic twelve-pointed star: frequently asked questions
The geometry
How is it constructed?
Two hexagons inscribed in the same circle, one turned 30° from the other. The first hexagon comes free — a compass set to the circle's radius steps around it exactly six times — and the second needs only that one arc be bisected. No measurement anywhere.
Where exactly is the dodecagon?
At r√3/2, 0.86603 of the radius, with its vertices on the hexagons' edge midpoints. That is not the same as the polygon where the two hexagons cross, which sits at 0.89658 and bounds the star's solid core. They are only about three percent apart here, but if you are placing an inner motif the distinction decides which number to work to.
Why is twelve-fold symmetry so common in Islamic ornament?
Because twelve divides by two, three, four and six, so a twelve-fold unit contains square, triangular and hexagonal symmetry at once. A designer can develop any of those inside the same star without the sub-pattern fighting the unit. Ten-fold gives you five and two; eight gives four and two. Twelve is the smallest fold that carries all three plane tilings.
Does a dodecagon tile the plane?
Not alone, but readily in company — with squares and triangles filling the gaps, in the semi-regular arrangements. That is the structure of a great many historical star patterns, with the twelve-pointed star sitting where the dodecagon would.
Is it true that Islamic patterns anticipated aperiodic tiling?
There is a real academic argument, it is contested, and it concerns a small number of specific decagonal patterns rather than twelve-fold work in general. Worth reading rather than repeating, and not something this figure demonstrates.
What historical evidence is there for the construction method?
Substantial. Surviving pattern scrolls — the Topkapı scroll among them — record the underlying compass-and-straightedge construction lines rather than only the finished designs, which is direct evidence of how the work was set out.
Why do my cut points come out blunt?
Twelve acute points are more fragile than eight, and a raster edge rounds every one of them. Export SVG for anything cut, fired or engraved — the failure only appears after the process rather than on screen.
Using it
How do I build a repeating field from it?
Place the units on a triangular lattice rather than a square one, so each star has six neighbours, and step by one diameter along three directions at sixty degrees. The gaps between neighbours are where the secondary pattern is developed. Register with the boundary circle — twelve near-identical points are easy to misalign by one.
How do I align it with an existing pattern?
Match the boundary circle to the motif's own circle, then rotate through the twelve positions until a point sits on a point. Twelve-fold symmetry is forgiving here — if it agrees at one rotation it agrees at all twelve, which is a quick way to confirm the pattern really is twelve-fold.
Export and print
Can I export the parts separately?
Yes. The hexagons, star, dodecagon and circle export as separate SVG paths depending on what you have switched on, which is what inlay and tile work need when the centre is a different material from the points.
What should I export for a laser cutter?
SVG, and check the point tips before you send it. Twelve points at a small size means twelve very acute angles, and an acute tip is where a laser overburns and a blade tears — scaling up or blunting the tips deliberately is often the right call.
Choosing a grid
When is eight-fold the better starting point?
When the field around it is square. Twelve-fold sits with hexagons and triangles; the eight-pointed star sits with squares and octagons, so the choice usually follows from the shape of the panel you are filling rather than from the star itself.
Should I build the field from this or from a hexagonal grid?
From a hex grid maker, with this placed on it. Twelve-fold stars do not tile the plane on their own — a dodecagon leaves gaps — so the underlying lattice is what makes a repeating field work, and the stars sit on its nodes.
Practical matters
Does my image get uploaded?
No. Everything happens in your browser — the image is drawn to a canvas on your own device and never sent anywhere.
Did Islamic patterns really anticipate aperiodic tiling?
Partly, and the claim is routinely overstated. Some fifteenth-century girih designs use tile sets whose subdivision produces near-Penrose configurations, which is a genuine and remarkable finding — but it is not evidence that the designers had a theory of aperiodicity. The published work says considerably less than the headlines did.
What evidence is there for how these were set out?
The Topkapı scroll and a handful of other pattern books show construction lines directly, which is unusually good evidence for a craft tradition. They indicate compass-and-straightedge work on an underlying polygonal grid — much as this overlay draws it.
Open the tool Twelve-pointed star generator
Two hexagons, twelve exact points
The Islamic 12 point star comes out of six compass marks and one bisection. Export vector or 600 DPI. No signup, nothing uploaded.
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