exactly 6 regular 4-polytopes
Theorem.exactly 6 regular 4-polytopes — sin(π/p)·sin(π/r) > cos(π/q) has exactly 6 Schläfli solutions.
Proof.Platonic cells + vertex figures + Schläfli sin(π/p)sin(π/r) > cos(π/q) leave {3,3,3} {3,3,4} {3,3,5} {3,4,3} {4,3,3} {5,3,3} — complete finite enumeration.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/thunder/waves/index.ts#discoveredTheoremsProvenWave
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
"exactly 6 regular 4-polytopes" 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 discoveredTheoremsProvenWave.
- 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 (discoveredTheoremsProvenWave @ src/thunder/waves) 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 discoveredTheoremsProvenWave (src/thunder/waves/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.