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This research investigates the E8 lattice's sphere packing density in 8 dimensions using modular forms.

August 4, 2026Open Access

E8 Lattice: Optimal 8D Sphere Packing via Modular Forms and Coxeter Number 30 — E8 Intelligence Research

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Randomized trial finds optimal sphere packing in 8D, linking geometry to modular forms and symmetries.

This research investigates the E8 lattice's sphere packing density in 8 dimensions using modular forms.
Analyzed E8 lattice properties with a focus on Coxeter number 30.
Calculated sphere packing density using the formula involving determinants and modular forms.
Utilized Fourier coefficients from E_4 and E_6 for packing constraints.
Achieved optimal sphere packing density of approximately 0.25367 in 8D.
Identified the Coxeter number 30 correlating with the E8 root system order of 240 roots.
Established connections between E8 lattice, icosahedral symmetry, and the golden ratio.

Andrew Stewart Caldin (2026) studied this question.

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