In his celebrated letter to Hardy in 1913, Ramanujan wrote down a continued fraction (independently discovered by Rogers twenty years earlier) and stated some remarkable evaluations of it for special values of \(\tau \in \mathbb {H}\) . Duke has explained Duke (2005) that these special evaluations arise because the Rogers-Ramanujan continued fraction is equivariant under the group G of rotations of the icosahedron. We show that this equivariance can be understood as an explicit bijection between the 6 vertex axes of the icosahedron and the 6 points in the projective line over the field with 5 elements. Moreover we show that just as rotations in G preserve the angles between the icosahedron axes, the transformations in \(PSL(2,5)\) preserve the cross ratios of the duad synthemes in the projective line.