On the Fibonacci Sequence of Pyritohedral Miller Indices and Its Correlation with Surface Reactivity of FeS2

The pyritohedral facets of iron pyrite (FeS2) with Miller indices {210}, {320}, {530}, {850}, and {13,8,0} form a Fibonacci sequence: their index ratios h/k = 2/1, 3/2, 5/3, 8/5, 13/8 are successive Fibonacci quotients converging to the golden ratio φ = (1 + √5)/2, the limit at which the pyritohedron coincides with the regular dodecahedron. Since the crystallographic restriction theorem forbids five-fold symmetry in periodic lattices, this limit is unattainable, and the Fibonacci facets are the closest crystallographically permitted approximations to it. This work compiles the available surface data for these facets and connects the Fibonacci index sequence to the facet-dependent surface reactivity of FeS2 for the first time. Published density functional theory and classical interatomic potential data are compiled for the two facets that have been characterized. The surface energy ordering {210} < {320} places the first two members of the sequence in a monotonically increasing series, and the DFT O2 adsorption energy on {210} (−3.87 eV) exceeds that on {100} (−0.80 eV) by a factor of 4.8, consistent with the reduced Fe surface coordination of the pyritohedron face. The three higher-order facets {530}, {850}, and {13,8,0} have not been characterized computationally or experimentally. The geometric analysis shows that the ratio of successive angular deviations of the Fibonacci facet normals from the dodecahedral direction (φ, 1, 0) converges exactly to φ² ≈ 2.618. Four falsifiable predictions are stated, of which this convergence rate is an exact mathematical result and the remaining three are testable by standard DFT slab calculations. The framework depends only on the pyrite crystal structure (space group Pa-3), not on chemical composition, and therefore extends to the more than 120 binary compounds, including CoS2, NiS2, and the skutterudites, that adopt this structure.---Ξυα Mσςςeva@m0ss.io