He is a pioneer in the introduction of five-fold symmetry in materials and in 1981 predicted quasicrystals in a paper (in Russian) entitled "De Nive Quinquangula"[3] in which he used a Penrose tiling in two and three dimensions to predict a new kind of ordered structures not allowed by traditional crystallography.

In a later manuscript, in 1982, he took the optical Fourier transform of a 2-D Penrose tiling decorated with atoms, obtaining a pattern with sharp spots and five-fold symmetry.

[5] For his contributions to quasicrystals in 2010 Mackay was awarded the Buckley Prize,[6] of the American Physical Society, with Dov Levine and Paul Steinhardt.

Mackay has been interested in a generalised crystallography, which can describe not only crystals, but more complex structures and nanomaterials.

[14] He produces scientifically inspired visual art under his artistic pseudonym Sho Takahashi.