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.

[7][8] He has applied his ideas of minimal surfaces to graphitic materials, proposing, with Humberto Terrones, periodic arrangements of carbon atoms with negative Gaussian curvature known as Schwarzites, which are the periodic cousins of Buckminsterfullerenes[9][10] Mackay has compiled a book of scientific quotations[11] and has co-authored a book on geometry with Eric Lord and S.