In 1962 he published a manuscript that showed how to pack atoms in an icosahedral fashion; a first step towards five-fold symmetry in materials science. These arrangements are now called Mackay icosahedra. 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” 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. This brought the possibility of identifying quasiperiodic order in a material through diffraction. Quasicrystals with icosahedral symmetry were found by Dan Shechtman and co-workers in 1984. For his contributions to quasicrystals in 2010 Mackay was awarded the Buckley Prize, of the American Physical Society, with Dov Levine and Paul Steinhardt. The Nobel Prize in Chemistry was awarded in 2011 to Dan Shechtman for the discovery of quasicrystals.
Mackay has been interested in a generalized crystallography, which can describe not only crystals, but more complex structures and nanomaterials. 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