Sacred geometry · The figure
What is Metatron’s Cube?
Metatron’s Cube is a figure made of 13 equal circles, called the Fruit of Life, with a straight line from every centre to every other centre: 78 lines in all. Inside those lines you can trace flat drawings of a cube, a tetrahedron, a star tetrahedron and an octahedron. The popular claim that all five Platonic solids are hidden in it does not hold for the other two, and you can test that below. The figure is named after Metatron, an angel of Jewish mystical writings whose name adds up to 314.
Showing
78 lines
Look for a solid
The last two buttons put a true dodecahedron and icosahedron over the figure, viewed the same way as the cube, to see whether their corners land on the 13 points.
How it is built
From the Flower of Life to 78 lines
Start with the Flower of Life and keep drawing past its border. Then pick 13 circles that just touch each other: one in the middle, six around it at two radii, and six more further out at four radii. Those 13 are the Fruit of Life.
Now join their centres. Each of the 13 points connects to the 12 others. That would count every line twice, so the total is 13 × 12 ÷ 2 = 78. The result looks like a cube drawn in perspective, which is where the word “cube” comes from.
The names are modern. MathWorld traces both “Fruit of Life” and “Metatron’s Cube” to Drunvalo Melchizedek’s 1999 book The Ancient Secret of the Flower of Life. The geometry is far older; the name is not.
The solids inside
Four solids fit. Two do not.
A flat drawing of a solid is a shadow of it. Hold a cube so one corner points straight at you and its outline is a hexagon with a Y inside. That exact drawing sits on the outer six points and the centre of Metatron’s Cube. So do a tetrahedron, the six-pointed star tetrahedron and an octahedron. MathWorld’s entry says so directly:
“Selected subsets of its line segments form familiar projections of the cube, octahedron, and tetrahedron. Claims that the same drawing gives exact projections of all five Platonic solids depend on the particular line segments and projections chosen and are not part of the definition.”MathWorld, “Metatron’s Cube”
The dodecahedron and icosahedron are the problem. Seen down the same axis, the icosahedron’s corners fall on two rings whose sizes are in the ratio 1.618, the golden ratio, but the figure’s rings are in the ratio 2. The dodecahedron needs twelve corners spaced around one ring; the figure has six points per ring. Press the last two buttons above and count: at best 8 of the dodecahedron’s 20 corners and 6 of the icosahedron’s 12 land on a point. Drawings that show them “inside” the cube add lines that are not among the 78.
This does not make the figure less interesting. It means the honest claim is four of the five Platonic solids, exactly.
Who Metatron is
The angel in the Talmud
Metatron is not in the Hebrew Bible. He appears in the Babylonian Talmud and in later Jewish mystical writings. In tractate Chagigah 15a, a sage ascending to heaven “saw the angel Mitatron, who was granted permission to sit and write the merits of Israel,” and wonders whether there are “two authorities” in heaven. To show there are not, the passage says, Metatron was taken from his place and struck with “sixty rods of fire.”
In Sanhedrin 38b, the verse in Exodus about an angel of whom God says “for My name is in him” is read as “referring to the angel Metatron, whose name is like the name of his Master.” Avodah Zarah 3b names Metatron as a teacher of schoolchildren.
The Book of Enoch. In the mystical work known as 3 Enoch, or the Hebrew Book of Enoch, Metatron explains who he once was: “Because I am Enoch, the son of Jared,” the man of Genesis who “walked with God” and was taken up to heaven.
The number
Why Metatron is 314
In gematria, each Hebrew letter is also a number. The medieval commentator Rashi, explaining “My name is in him” in Exodus 23:21, writes that the angel is Metatron, “whose name is even as the name of his Master, for מטטרון has the numerical value of שדי, the Almighty.” Count it in the box above: מטטרון is 40 + 9 + 9 + 200 + 6 + 50 = 314, and Shaddai, שדי, is 300 + 4 + 10 = 314.
There is a catch worth knowing. The Talmud passages spell the name with an extra letter, מיטטרון, which adds 10 and makes 324. The 314 match works in Rashi’s shorter spelling, which is the one gematria tradition uses.
What is proven
Metatron’s Cube, sorted
| Claim | Status |
|---|---|
| It has 13 circles and 78 lines. | Real · 13 × 12 ÷ 2 |
| A cube, tetrahedron and octahedron are inside it. | Real · as flat drawings |
| All five Platonic solids are inside it. | No · dodecahedron and icosahedron miss |
| Metatron appears in the Talmud. | Real · Chagigah 15a, Sanhedrin 38b |
| Metatron appears in the Bible. | No · not in the Hebrew Bible |
| Metatron and Shaddai both equal 314. | Real · Rashi on Exodus 23:21 |
| The name “Metatron’s Cube” is ancient. | No · modern, from 1999 |
Questions
Metatron’s Cube
What is Metatron’s Cube meaning?
In modern sacred geometry it is presented as a figure that holds the basic shapes of the physical world, the Platonic solids, and is linked to the angel Metatron. As geometry, it is 13 equal circles with all 78 lines between their centres, and it contains exact drawings of four of the five Platonic solids.
How many lines are in Metatron’s Cube?
78. Each of the 13 circle centres is joined to the 12 others, and 13 × 12 ÷ 2 = 78.
Does Metatron’s Cube contain all five Platonic solids?
No. It contains exact flat drawings of the cube, tetrahedron, octahedron and star tetrahedron. A true dodecahedron or icosahedron does not fit its 13 points: at best 8 of 20 and 6 of 12 corners land on one.
What number is associated with Metatron?
314. In Hebrew gematria, מטטרון (Metatron) is 40 + 9 + 9 + 200 + 6 + 50 = 314, the same as שדי (Shaddai, the Almighty), a link Rashi records in his commentary on Exodus 23:21.
Who is Metatron?
An angel of Jewish tradition, not of the Hebrew Bible. The Talmud describes him as a heavenly scribe whose name is like his Master’s, and the Hebrew Book of Enoch says he was once Enoch, the son of Jared.
Is Metatron’s Cube in the Bible?
No. Neither the figure nor the angel Metatron appears in the Bible. The angel comes from the Talmud and later mystical books; the figure and its name date from the 1990s.
Sources
Where this comes from
- Eric W. Weisstein, “Metatron’s Cube” and “Fruit of Life,” MathWorld: mathworld.wolfram.com.
- Babylonian Talmud, Chagigah 15a, William Davidson edition, Sefaria: sefaria.org.
- Babylonian Talmud, Sanhedrin 38b, Sefaria: sefaria.org.
- Babylonian Talmud, Avodah Zarah 3b, Sefaria: sefaria.org.
- Rashi on Exodus 23:21, translated by M. Rosenbaum and A. M. Silbermann, Sefaria: sefaria.org.
- Hugo Odeberg, 3 Enoch or the Hebrew Book of Enoch, Cambridge University Press, 1928: archive.org.
- “Metatron,” Encyclopaedia Britannica: britannica.com.
- Joseph Jacobs and Ludwig Blau, “Meṭaṭron,” Jewish Encyclopedia, 1906: jewishencyclopedia.com.
- Eric W. Weisstein, “Platonic Solid,” MathWorld: mathworld.wolfram.com.
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Metatron’s Cube with your chosen solid, printed large.