Metatron’s Cube
Make Metatron’s cube at an exact size: the 13 circles of the fruit of life and all 78 lines joining their centres. Start from one of our 16 designs: classic, lines only, join-the-dots, the cube or two nested cubes picked out, the octahedron, the hexagram, a bold colouring page, a light grey tracing sheet or gold on navy. Switch the circles, lines and dots, set the line width and colours, add a ring and set the size across in inches or centimetres on US Letter or A4. Print one big figure, a sheet of small ones, or the drawing steps. Download a PDF, 300 DPI PNG or SVG. Nothing is uploaded.
100% private — everything runs in your browser. Everything runs in your browser; nothing is uploaded.
Print at 100% (Actual size). Dashed lines in the cube and octahedron are the edges hidden behind the solid. Use the light grey look for a tracing sheet, or the bold outlines to colour in.
Figure
Lines and colours
Size and paper
Runs in your browser with our own code: nothing you type is uploaded or saved. The figures are our own drawings. You may use what you make here, including commercially, with no credit needed.
How to make and print Metatron’s cube
- Pick a design to start from: classic, lines only, join the dots, a solid picked out, colouring or tracing.
- Switch the 13 circles, the 78 lines and the centre dots on or off.
- Pick out a cube, two cubes, the octahedron, the hexagram or the two hexagons if you want.
- Set the line width, colours, size across and paper.
- Download the PDF and print at 100% (Actual size), or the SVG for a cutting machine.
What you can use it for
- Colouring pages and tracing sheets
- Join-the-dots drawing practice with a ruler
- Geometry lessons: hexagons, projections and solids
- Wall art, posters and stencils
- SVG files for laser cutting, engraving and vinyl
- Tattoo and jewellery sketches
The 16 Metatron’s cube designs
| Design | Circles | Lines | Dots | Picked out | Look | Layout |
|---|---|---|---|---|---|---|
| Metatron’s cube: 13 circles and 78 lines | 13 | 78 | – | None | Coloured lines | One per page |
| Lines only, with centre dots | – | 78 | Yes | None | Coloured lines | One per page |
| Join the dots: 13 circles and centres, no lines | 13 | – | Yes | None | Coloured lines | One per page |
| With the cube (inner hexagon) picked out | 13 | 78 | – | Cube (inner hexagon) | Coloured lines | One per page |
| With two nested cubes | 13 | 78 | – | Both cubes (nested) | Coloured lines | One per page |
| With the octahedron (outer hexagon) | 13 | 78 | – | Octahedron (outer hexagon) | Coloured lines | One per page |
| With the hexagram (two triangles) | 13 | 78 | – | Hexagram (two triangles) | Coloured lines | One per page |
| With the inner and outer hexagons | 13 | 78 | – | Inner and outer hexagons | Coloured lines | One per page |
| In a ring (enclosing circle) | 13 | 78 | – | None | Coloured lines | One per page |
| Colouring page: bold outlines | 13 | 78 | – | None | Coloured lines | One per page |
| Tracing sheet: light grey lines | 13 | 78 | – | None | Light grey (tracing) | One per page |
| Gold on navy | 13 | 78 | – | None | Coloured lines, dark background | One per page |
| Turned 30° (flat top) | 13 | 78 | – | None | Coloured lines | One per page |
| Lines only with the cube | – | 78 | – | Cube (inner hexagon) | Coloured lines | One per page |
| Drawing steps | 13 | 78 | – | None | Coloured lines | Construction steps |
| Sheet of small cubes | 13 | 78 | – | None | Coloured lines | Sheet of small ones |
All are our own drawings. Every design is a starting point: switch the circles, lines and dots, pick out a solid and change the colours. Our tests check the 13 centres, that there are exactly 78 lines and each joins two of them, and that the cube and octahedron are exact views of the solids.
The 78 lines by length
| Length | In circle radii | Lines |
|---|---|---|
| 2 r | 2.000 r | 18 |
| 2√3 r | 3.464 r | 18 |
| 4 r | 4.000 r | 15 |
| 2√7 r | 5.292 r | 12 |
| 6 r | 6.000 r | 6 |
| 4√3 r | 6.928 r | 6 |
| 8 r | 8.000 r | 3 |
Lengths are in circle radii (r). The inner hexagon has sides of 2 r and the outer hexagon sides of 4 r; the longest lines (8 r) cross the whole figure through the middle.
Drawing steps
| Step | What to do | Circles | Lines |
|---|---|---|---|
| 1 | Draw a circle. Step the compass round it to mark six points 60° apart, then draw six circles of the same size touching it: their centres are 2 radii from the middle. | 7 | 0 |
| 2 | Draw six more circles straight outward, centres 4 radii from the middle: the 13 circles of the fruit of life. | 13 | 0 |
| 3 | Join the middle to the 12 other centres (12 lines). | 13 | 12 |
| 4 | Join the inner six in a hexagon and the outer six in a hexagon (24 lines so far). | 13 | 24 |
| 5 | Join every remaining pair of centres: 78 lines in all. | 13 | 78 |
The steps are made from the same circles and lines as the finished figure: each step contains the one before, and the last step is the figure you print.
Sizes
| Paper | Largest figure, portrait | Landscape |
|---|---|---|
| US Letter | 7.5 in (19 cm) | 7 in (17.8 cm) |
| A4 | 7.25 in (18.4 cm) | 6.75 in (17.2 cm) |
| Size across | Circle radius: classic flower | 19 circles, no ring | Seed of life in a ring | Metatron’s cube |
|---|---|---|---|---|
| 4 in (101.6 mm) | 16 mm | 16.9 mm | 25.4 mm | 10.2 mm |
| 6 in (152.4 mm) | 24 mm | 25.4 mm | 38.1 mm | 15.2 mm |
| 7.5 in (190.5 mm) | 30 mm | 31.8 mm | 47.6 mm | 19.1 mm |
Every page has a 1 in (or 2 cm) bar at the bottom to check the print is at 100%. For a wall-size print, use the Poster Tiler; to measure angles on screen, the Online Protractor.
Picked-out figures
| Pick out | What it is | Exact? |
|---|---|---|
| Cube (inner or outer hexagon) | A cube seen straight down a long diagonal: hexagon outline, 3 edges seen, 3 hidden (dashed) | Yes: projection of the 12 cube edges |
| Octahedron (outer hexagon) | An octahedron seen down a 3-fold axis: hexagon outline, front triangle, back triangle (dashed) | Yes: projection of the 12 edges |
| Hexagram | Two equilateral triangles on the outer six points | Yes: a flat figure |
| Two hexagons | The inner and outer hexagons | Yes: a flat figure |
All picked-out lines are among the 78 lines. Tetrahedron, icosahedron and dodecahedron views are not drawn, because they need points that are not among the 13 centres.
What prints
| Download | What is in it |
|---|---|
| Every page at real size, vector: circles, arcs, rings, lines and the size bar | |
| PNG 300 DPI | One picture per page (a ZIP when there are several) |
| SVG | The page on screen at real size, with circles, lines, rings and overlays in separate groups (good for cutting machines and laser cutters) |
Which tool to use
| You want | Use |
|---|---|
| The flower of life, seed, egg or fruit of life | Flower of Life (with construction steps) |
| Metatron’s cube, its 78 lines and the cube inside it | Metatron’s Cube |
| Your own radial design drawn by hand with mirror symmetry | Mandala Maker |
| Looping curves from a ring and a wheel | Spirograph Generator |
| Seamless star-and-polygon tilings | Islamic Geometric Pattern Generator |
The Mandala Maker mirrors whatever you draw round a centre, the Spirograph Generator draws roulette curves, and the Islamic Geometric Pattern Generator builds repeating star tilings. None of them places circles on an exact lattice: this page does, so the circle radius and every crossing are exact.
More free tools
Patterns, symmetry and round designs?
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Frequently asked questions
What is Metatron’s cube?
A flat figure made from 13 points: a centre and two hexagons of six points round it, the outer one twice as far out and in line with the inner one. Every point is joined to every other, which gives 78 lines. The 13 points are the centres of the 13 circles of the fruit of life.
Why 78 lines?
Each of the 13 points joins the 12 others: 13 × 12 = 156, and each line is counted twice, so 156 ÷ 2 = 78. Some lines lie on top of each other along the same straight path (for example middle to inner point to outer point), so fewer separate strokes show.
Where is the cube in Metatron’s cube?
Join the inner hexagon and three lines from the middle to every other corner: that is exactly how a cube looks when you view it straight down a long diagonal. The other three lines from the middle are the hidden edges at the back, drawn dashed. The outer hexagon holds a bigger cube the same way.
Does it contain the Platonic solids?
Some views are exact: the cube (inner or outer hexagon) and the octahedron (outer hexagon with one triangle in front and one behind) are true flat views of those solids along a 3-fold axis, and our tests rebuild them from 3-D corners. We do not draw the others because they need points that are not among the 13 centres.
How do I draw Metatron’s cube?
Draw a circle and six touching circles round it (centres 2 radii out), then six more straight outward (4 radii out). Mark the 13 centres and join them with a ruler: the middle to all 12, then the two hexagons, then every remaining pair. The drawing steps layout prints this in pictures.
Where does the name come from?
Metatron is an angel named in later Jewish mystical writings. The name Metatron’s cube for this figure comes from modern esoteric books. This page treats it as geometry and art and makes no claims about powers or energy.
How big can I print it?
Up to 7.5 in (19 cm) across on US Letter portrait and 7.25 in (18.4 cm) on A4 portrait. For a bigger print, download the SVG and tile it over several sheets.
Can I use it for a cutting machine or laser?
Yes. Download the SVG: it is at real size, with circles, lines and overlays in separate groups.
Is it free?
Yes. There is no sign-up, no watermark and no limit.
Is anything uploaded?
No. The figure is drawn by JavaScript in your browser. Nothing you choose is sent anywhere or saved when you close the page.