The alternating group of degree 5 and the icosahedron rotations: seeing not only proving

TL;DR

This paper explores the relationship between the 60 rotations of the icosahedron and the permutations of the alternating group A5, emphasizing a visual and conceptual understanding over purely logical proofs.

Contribution

It establishes a bijection between icosahedron rotations and A5 permutations, highlighting a more intuitive approach to group isomorphism.

Findings

Bijection between icosahedron rotations and A5 permutations

Enhanced understanding of group structure through geometric visualization

Bridging abstract algebra with geometric intuition

Abstract

When compared with pure mathematicians, applied ones have a clear preference for proofs that go beyond a chain of reasonings and do exhibit the fact to be proved. Here we exhibit the bijection between the 60 icosahedron rotations of the group R and the 60 permutations of the group A5.