Golden Icosahedron

analytical · neon · twelve laws · under keeper eris

neon

{{ act || react || change }} · the sculpture

analytical

Twelve vertices at the cyclic copies of (0, plus or minus 1, plus or minus phi) share one radius, meet in thirty edges, and phi squared equals phi plus one.

LIT φ = (1 + √5) / 2 and φ² = φ + 1. The twelve points are (0, ±1, ±φ) and the two cyclic permutations. They lie on one sphere. The shortest distance among the 66 pairs occurs 30 times, which is the icosahedron's edge count.

AMBER The regular icosahedron and the golden ratio have been tied together since antiquity. The coordinate list used here is the standard modern one. The check builds the points itself.

MODEL Vertices are lamps. Rods join only the thirty nearest pairs. The group yaws so the triangle faces come around. One yaw, taken from the group's own rotation.

Sources AMBER

  1. Regular icosahedron (reference)

LIT on load: the identity is recomputed (it throws on mismatch), the training target scores 1, 200 rounds improve the shared sketch, the workspace loop logs 5 entries, and the OBJ and SVG exports match the sketch.

Gallery of kept sketches:

Workspace improvement loop MODEL

  1. Measure: every 40 rounds, record the acceptance rate, the current score and how many rounds since the last improvement.
  2. Try next: if the score has been flat for 40 rounds, widen the mutation step. If acceptance is under 15%, shrink it; over 45%, widen it. Otherwise keep it.
  3. Log back: append {entry, round, measured, tried, step} to the workspace log (it is in the export JSON and the list below).
  4. Repeat: re-check the identity before claiming it. The seal stays write-if-missing.

Live workspace log:

    Shared board MODEL

    localStorage key mayhem-twelve-laws-board. Each page writes its best shared reward.

      Attempt board MODEL

        ← Vis-Viva · Twelve Laws · ERIS

        Background wash: AMBER MODEL a field seeded from this page's seal. The viewport is a deep colour, not black, over a vivid page.

        proving…

        Seal sha256(name|slug|blurb): 690bcc49df6403f9f2166b2909f8ca3b2c5bd9e0d33297c9d79371c54dcf6522