Geodesic dome closure
Theorem.Geodesic dome closure — the φ-icosahedron subdivided at frequency ν closes Euler V−E+F=2 with V=10ν²+2, E=30ν², F=20ν²; every strut obeys the one chord law 2R·sin(θ/2) (verified to 10⁻¹⁵) and 3 strut classes suffice at ν=3.
Proof.the φ-icosahedron subdivided at frequency ν closes Euler V−E+F=2 with V=10ν²+2, E=30ν², F=20ν²; every strut obeys the one chord law 2R·sin(θ/2) (verified to 10⁻¹⁵) and 3 strut classes suffice at ν=3.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/6/4/index.ts#geodesicDomeComputes
1 · Classification
finite-complete — self-contained computation, no external lean
2 · Provenance
Documented theorem re-derived by exhaustive computation (humanityNovel=false); first-in-this-registry is the only sense of discovered.
Acknowledgment
"Geodesic dome closure" is a re-derivation, acknowledged to documented mathematics — the original proof is the prior art this re-derivation acknowledges; not new to humanity — the contribution is the reproducible computation geodesicDomeComputes.
- Prior art
- documented mathematics — the original proof is the prior art this re-derivation acknowledges
- Novelty
- not new to humanity — a re-derivation (humanityNovel = false)
- Contribution
- a reproducible computation (geodesicDomeComputes @ src/6/4) that re-derives the result at zero tokens — the contribution is the verifiable recomputation, NOT the theorem
3 · Reproducibility
Recompute from source: npm run theorems:verify recomputes geodesicDomeComputes (src/6/4/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.