Base 60 and the Icosahedral Factorization of Coordinate Space

This work establishes a minimality property of the positional base 60 grounded in the classification of finite subgroups of SO(3). Among these subgroups, the icosahedral group A₅ ≅ I of order 60 is the unique simple non-abelian member. Two notions of admissible group structure on a digit set are formulated — one requiring realization as a subgroup of SO(3), the other requiring only a faithful irreducible three-dimensional real representation — and shown to be equivalent for simple non-abelian groups. The minimal admissible base is b = 60, attained uniquely by A₅. The digit set {0, …, 59} is placed in bijection with A₅, and digit sequences are read as walks in the Cayley graph, equivalently as paths in the…