Euler's Count

analytical · neon · twelve laws · under keeper eris

neon

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

analytical

Vertices minus edges plus faces is two for the tetrahedron, the cube and the icosahedron.

LIT Tetrahedron 4 − 6 + 4 = 2. Cube 8 − 12 + 6 = 2. Icosahedron 12 − 30 + 20 = 2. The page adds those integers. It does not ask the graphics library how many vertices it welded.

AMBER Euler's formula for convex polyhedra, V − E + F = 2, dates to 1758. It fails for a torus (that characteristic is 0). These three solids are convex.

MODEL An icosahedron, a cube and a tetrahedron share the room. The spin is only so the faces can be seen.

Sources AMBER

  1. Euler characteristic (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

        ← Kepler's Cubes · Twelve Laws · One Fourier Bin → · 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): 8310cd947c49c33ab48e79441cd1b386da2210a6f655d45a684ceae391a957d5