The interactive reference
The cuboctahedral Vector Equilibrium is generated from permutations of (0, ±1/√2, ±1/√2). Its twelve radii and twenty-four edges are equal. There are eight equilateral triangular faces and six square openings. A selected face is highlighted in its actual projected position. Motion of the pointer rotates the view, not the object’s internal relationships.
Expansion and contraction
The −1 and +1 controls select the contracted tetrahedron and expanded cuboctahedron. The 0∞ control repeatedly travels between them; ve returns to the Vector Equilibrium. The three named stations are tetrahedron, icosahedron and cuboctahedron. The octahedron is retained as an intermediate geometric junction, not removed from the path.
The first segment uses counter-rotating equilateral triangles and axially moving face centres. The regular icosahedral station occurs at 22.238756092964948 degrees; the octahedral junction occurs at 60 degrees. The six temporary dotted icosahedral diagonals close the remaining triangular surfaces; they are not additional rigid bars.
The tetrahedral segment is a numerically constructed continuation with twelve shared labelled joints and twenty-four unit-length edges. At the endpoint these coincide into four spatial vertices and six edges; every tetrahedral face carries two original triangles. The stored frames preserve squared edge lengths to better than 2 × 10⁻¹³. Linear interpolation between stored frames introduces a small numerical approximation, checked separately in the test report. This is an articulated geometric path, not a simulated force, energy or physical scale-transition model.
The continuation is our numerical linkage construction, not a claim that its particular intermediate coordinates are Fuller’s unique hand-operated motion. Fuller describes the cuboctahedral, icosahedral, octahedral and tetrahedral sequence in Synergetics, sections 460–461. R. W. Gray describes the symmetric segment in The Jitterbug Motion.
Recording and timing
The original prologue and three book recordings are unchanged and remain hosted in the original Zero Infinity archive. This edition uses their published transcript cues. Some chapter labels occur within a cue; the chapter jump uses that cue’s start. Drawings follow cue-level anchors, not a new word-level alignment. The transcript appears only a short passage at a time.
The silent companion uses a separate local clock. Its QR link carries the reading device’s current time and playback rate. Rescan after a pause, seek or speed change; there is no microphone or background tracking.
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