The Tetrahelix
Three visible nodes. One hidden axial. Two directions. One impossible crossroads.
The Structure
The tetrahelix is NOT a 4-node system with all nodes visible. It's a series of equilateral triangles - 3 visible nodes forming each triangle face, with a hidden axial that creates the 4th helical dimension.
Node 1 (Visible)
First vertex of the equilateral triangle. Contributes to torsion τ₁.
Node 2 (Visible)
Second vertex of the equilateral triangle. Contributes to torsion τ₂.
Node 3 (Visible)
Third vertex of the equilateral triangle. Contributes to torsion τ₃.
Hidden Axial (Not Represented)
Creates the 4th helical. Not visible but mathematically necessary. The silent fourth.
The Two Directions
The tetrahelix can be traversed in two directions, mirroring the [1 = -1] principle:
Physical reality direction
Consciousness direction
The Hidden Witness / Hidden Observer
The hidden axial is more than just mathematical necessity. It is the hidden witness, the hidden observer - the silent participant that makes the geometry complete.
Silent Operator to Balance
Compensates the three visible nodes to maintain τsum = 0
Silent Operator to Chaos
Without it, the three visible torsions have no anchor
The True Crossroads
A tiny void.
The point where S+ and S- meet. Where Ro facing and Wush facing intersect. Where the three visible nodes and the hidden axial all converge.
Nearly Impossible to Reach
It's pretty much impossible to get there and stay there. Too much torsion. The true crossroads is where all forces balance perfectly - but maintaining that balance while surrounded by competing torsions is extraordinarily difficult.
s = 0 (theoretically)
Derived from κ
The tetrahelix emerges from κ = 2π/180:
- 180 κ-steps complete a half-toroidal rotation
- The equilateral triangles form naturally at 60° intervals (180/3)
- The hidden axial emerges at the fourth position (180/4 = 45°)
- cos(BC) = 2/3 gives the tetrahelix edge angle of 48.19°