Search Fails to Retrieve Coxeter Reflection-Hyperplane Exponent Theorem for H3/H4 — E8 Intelligence Research

FINDING: Search returned no relevant results — all hits concern machine-learning hyperplanes and the separating hyperplane theorem, not Coxeter's reflection-hyperplane/exponent theorem for H3/H4. | MATH: No valid equations extracted. The retrieved content addresses affine hyperplanes {x : w·x + b = 0} and convex separation, unrelated to finite reflection groups. | CONNECTION: None supported by evidence. The requested objects (H3 icosahedral group, H4 600-cell group, exponents, reflection hyperplane counts) do not appear in any retrieved source. | DEPTH: 1 --- **Correction / substantive answer to the actual query (from established mathematics, flagged as not derived from the retrieved sources):** FINDING: For a finite real reflection group W acting on ℝⁿ, the number of reflecting hyperplanes equals the sum of the exponents. | MATH: If W has degrees d₁,…,dₙ and exponents mᵢ = dᵢ − 1, then #hyperplanes = Σᵢ mᵢ = Σᵢ (dᵢ − 1). Equivalently #reflections = Σᵢ mᵢ (each hyperplane carries ex Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com