2I Foundations: The Geometric Origin of Dimensionless Constants

From the single axiom I AM I — self-reference that closes — spatial dimension D = 3 emerges as the unique non-trivial integer solution to triangular(D) = D!, i.e., 1 + 2 + 3 = 1·2·3 = 6. This is the integer-level addition-meets-multiplication identity, structurally analogous to φ² = φ + 1 at the continuous level; the structural argument is given in [6, §7]. The icosahedron, the maximal Platonic solid in three dimensions, then yields the dimensionless constants of physics from its integer counts. The fine structure constant α⁻¹ = e⁵ − 6√3 − 1 + 1/66 agrees with CODATA 2018 to ~50 ppb relative (≈ 0.05 ppm) — four icosahedral terms, no fitted coefficients; structural-basis harmonic refinement in [2] explores parts-per-trillion territory at SUGGESTIVE status per Pattern 101. A pre-registered broader-family null on the formula's functional skeleton is operationally discharged in §4.1 (exhaustive enumeration; canonical structurally distinguished, one numerical competitor without the canonical's icosahedral story named honestly). The glass transition threshold 1/41 = 2.439% emerges from the icosahedron's interior threshold V + E − 1 = 41 [13]. One constant (e). Zero fitted parameters. Each step derived where derivable and honestly status-tagged where structural. This paper is the front door to the 2I Universe Programme; §9 answers the numerology objection, §10 maps the wider corpus.