Leech Lattice: Unifying 24D Geometry, M24 Group, Higman-Sims Graph, and K3 Surfaces — E8 Intelligence Research

July 21, 2026Open Access

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This research aims to explore the relationships between the Leech lattice, the M24 group, and K3 surfaces, revealing their interconnected geometries.
Analysis of the Leech lattice Λ₂₄ and its properties, including its minimal vectors and norms.
Examination of the automorphism groups related to the Leech lattice and the Higman-Sims graph.
Utilization of Conway's simple method for constructing the lattice using the binary Golay code.
Identified 196560 minimal vectors in the Leech lattice with a minimal norm of 4.
Established connections between the Leech lattice, M24 group, and Higman-Sims graph with specific properties.
Demonstrated that the kissing number of the Leech lattice is the highest known in 24D.

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Finding unifies 24D geometry, group theory, and algebraic surfaces, suggesting deep structural links in mathematics.

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Andrew Stewart Caldin (2026) studied this question.

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