Step 2 of 4
Explore the Structure
Look at the construction, its points and its distances. Ratios between distances are what become frequencies.
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Geometry structure
The complete construction, whatever is shown in the drawing.
9
Points
shown
1
Circles
shown
12
Lines
shown
Measurements & ratios 3
Each length divided by the reference length gives a ratio r. These ratios become frequencies in the next step.
| Measurement | Length | Ratio r |
|---|---|---|
| |P0P5| | 1.1547 | 1.0000 |
| |P0P1| | 1.6330 | 1.4142 |
| |P0P4| | 2.0000 | 1.7321 |
Mathematical details
Two regular tetrahedra: T₁ on alternate cube vertices (1,1,1),(1,−1,−1),(−1,1,−1),(−1,−1,1) and T₂ = −T₁. Edges are drawn within each tetrahedron only. Circumradius R.
Symmetry: Octahedral Oh (compound).
Symbolic interpretation
The term derives from Hebrew merkavah (chariot); its 'light-body' meanings come from modern esoteric writing.