TriLateral braiding introduces a third directional system. Strands interact along the X, Y, and Z axes, creating a spatial braid structure.
In the previous entry we described a braid as a repeating pattern created by strands crossing in opposite directions. Those crossings occur primarily across two directions, which can be described as movement along the X and Y axes.
The illustration above introduces a third directional movement: Z.
When strands interact along three axes instead of two, the braid becomes TriLateral. In this system, strands moving in the X and Y directions are intersected by strands moving along the Z direction. The structure is no longer only a flat surface interaction—it becomes a spatial braid system.
A TriLateral braid repeated across a fabric surface. Each repeating unit contains strand crossings in the X, Y, and Z directions.
When the TriLateral crossing repeats, a continuous lattice forms. The repeating structure contains strands traveling diagonally across the fabric while a third strand system weaves through them. Each repeat contains crossings that occur above and below the central plane of the structure.
This introduces a layered interaction within the braid. Instead of a single crossing plane, the structure contains upper and lower crossings along the Z direction.
Upper and Lower Crossings
Within the TriLateral unit, the Z-direction strand alternates between two positions:
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Upper Z crossing – the strand passes above the central crossing plane
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Lower Z crossing – the strand passes below the central crossing plane
This alternating movement stabilizes the braid while allowing strands to interact through the structure.
Why This Matters
Understanding braids through X, Y, and Z directional movement helps describe lace braiding as a structured pattern system rather than simply a decorative textile technique.
When these directional rules are controlled, braids can be engineered to create structures that expand, compress, or distribute load. The braid becomes a programmable lattice rather than just a fabric.