This work establishes a minimal base 60 using icosahedral group properties, suggesting new encoding methods for symmetric systems.
Key Points
This research aims to explore the minimality of base 60 through the lens of the icosahedral group A₅ and its properties in three-dimensional representations.
Established properties of the icosahedral group A₅ within the group SO(3).
Formulated two notions of group structure for base 60 digit sets and demonstrated their equivalence.
Constructed bijections between the digit set {0, …, 59} and A₅, analyzing properties through Cayley graphs.
Identified that base 60 uniquely represents the icosahedral group A₅.
Showed equivalence of group structures for simple non-abelian groups in this context.
Proposed an alternative encoding scheme for discrete orientations utilizing finite-group multiplication.