One measure
Twenty-four struts and twelve radii, and at the vector equilibrium every one of them is the same number. Nothing in the structure is held harder than anything else.
Twelve around one.
At equilibrium, twelve spheres close around a thirteenth and every length in the structure is the same measure: each strut, each radius, one number. Nothing is holding it together. It is only the shape the forces make.
- Move, and the light followsDrag, and the light follows
- Draw in, and the field closesDrag to centre to close it
Phase 0.000 · Vector equilibrium
24 struts · 12 + 1 · 0 closing
Forming the field
The jitterbug
Hold the struts rigid and turn the eight triangles. The square faces fold shut, the twelve vertices spiral inward, and the cuboctahedron becomes an icosahedron without one strut changing length.
Twelve, not thirteen
Twelve is the greatest number of equal spheres that can touch a thirteenth at once. There is no fourteenth position to take. The number is not a choice anyone made.
The matrix
Repeat the arrangement and it fills space with no gaps and no privileged direction. Every point identical, every vector equal. Fuller called it the isotropic vector matrix.
Equal in every direction. That is the whole of it.
Two hands
The jitterbug turns either way. Twist the eight triangles one way and the twelve vertices spiral into an icosahedron; twist them the other and you get its mirror. The vector equilibrium is the single moment where both hands are the same shape.
What comes next
Keep turning past the icosahedron and the vertices meet in pairs: twelve become six, and the icosahedron closes into an octahedron. Fold that and you have a tetrahedron. One motion, four solids, no strut ever changing length.
The zerophase
The vector equilibrium cannot stand up. Its six square faces are not triangulated, so nothing in it resists a shear and it holds no shape of its own. Fuller called it the zerophase: not a structure, but the condition structures pass through.