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'Metatron's Compass' is a unique geometry in many ways. It can also be named 'the 4 Dimensional Vector Equilibrium', 'the 4 dimensional CubeOctahedron', or 'the Toroidal projection of the 24 Cell Polytope', but I prefer to call it Metatron's Compass as I believe it is the secret behind the popular 2 dimensional design known as Metatron's Cube.
The importance of Metatron's Cube lies in its unification of the various possible symmetries of space, as shown in the way that the outlines of the 5 Platonic solids can be found within the 2 dimensional pattern. It also makes visible concepts related to maximum stability and minimum entropy, optimal sphere packing, and fractal containment of its own form.
Wearing this form or having it in your space is healing and balancing of any disturbances as it aligns with the fundamental structure of space and time and radiates source energies into its environment. Metatron is the name of an 'Archangel' said to be 'God's Scribe' who takes the divine utterances and gives them comprehensible form before transmitting them into creation.
I have created a web page about Metatron's Compass on www.SacredGeometryWeb.com called The 24 Cell is the 4D Vector Equilibrium and a page explaining the symbology called Mysticism & Metatron
The 24 cell has 24 vertexes, 24 octahedral faces, 96 edges, 96 equilateral triangular faces, 12 cubeoctahedral cross sections, 12 rhombic dodecahedrons, and at least 12 cubes and 3 hypercubes. The distorted outline of ALL of these shapes can be found within Metatron's Compass, and the bounding figure of this projection is the Toroidal Hypercube that is also available in our Shapeways SacredGeometryWeb shop.
Technically this form is a new projection of one of the six 4 dimensional Platonic solids known as 'the 24 cell polytope'. The 24 cell combines the Cubic and Octahedral symmetries in one form and is a unique geometry in at least 3 ways.
1) It is the only non tetrahedral form in any dimension that is its own 'dual' which means that its 24 octahedra can be exchanged with its 24 vertexes to create a new version of itself.
2) It is the only non cubic form in any dimension that can tile space without rotation.
3) It is the only Platonic solid in any dimension that is also a Vector Equilibrium
I recommend this 5cm diameter version in Raw Brass, or Gold Plated Brass.
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