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Metatron's Cube


MetatronsCube

Metatron's cube is a plane geometric figure formed from 13 points arranged as a central point together with two concentric regular hexagons, with every pair of points joined by a line segment. The resulting line drawing is the straight-line drawing of the complete graph K_(13) on these specially placed vertices, and therefore contains

 (13×12)/2=78,

line segments before coincident subsegments are combined visually.

In the modern terminology used by Melchizedek (1999, pp. 158-160), the 13 points are the centers of the 13 circles in the fruit of life, a selection from an extension of the flower of life pattern. The seven-circle seed of life is an earlier subconfiguration of the same overlapping circles grid.

The figure is commonly drawn together with 13 congruent circles centered at the points. It has sixfold rotational symmetry and reflection symmetry, and 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.


See also

Complete Graph, Cube, Flower of Life, Fruit of Life, Octahedron, Overlapping Circles Grid, Platonic Solid, Seed of Life, Tetrahedron

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References

Melchizedek, D. The Ancient Secret of the Flower of Life, Volume One. Flagstaff, AZ: Light Technology Publishing, pp. 158-160, 1999.

Cite this as:

Weisstein, Eric W. "Metatron's Cube." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MetatronsCube.html

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