Li — Experiment A: Voronoi Hopf | PAPP

3D Model

Li — Experiment A: Voronoi Hopf (PAPP V5) is a watertight high-relief disc where 4D polychoron vertices, projected through Hopf (S³→S²), become Voronoi seeds on the disc.

A furthest-point subsampling selects 150 seeds from the full 42,852 projected vertices (7 Li polychora), producing a hard, binary tessellation: every surface point belongs to exactly one cell.

Height is built from (1) cell plateau driven by the source polychoron’s β* (normalized to ~0.5–0.9), (2) surface roughness from the Pythagorean ratio a/c, (3) geological cell tilt, and (4) sharp broken valleys at boundaries using a sigmoid transition (depth 0.35, width 0.06).

Adds Pythagorean frequency modulation and Hopf fiber rings (n=1–5).

Mesh: 57,170 verts / 114,336 faces, closed manifold χ=2. Z range [−0.110, 1.051]. Unique colors (3dp): 22,344.

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