
de Bruijn’s pentagrids (2)
Last time we’ve seen that de Bruijn’s pentagrids determined the vertices of Penrose’s P3aperiodic tilings. These vertices can also be obtained by projecting a window of the standard hypercubic lattice $\mathbb{Z}^5$ by the cutandprojectmethod. We’ll bring in representation theory by forcing this projection to be compatible with a $D_5$subgroup of the symmetries of $\mathbb{Z}^5$, which […]

de Bruijn’s pentagrids
In a Rhombic tiling (aka a Penrose P3 tiling) we can identify five ribbons. Opposite sides of a rhomb are parallel. We may form a ribbon by attaching rhombs along opposite sides. There are five directions taken by sides, so there are five families of ribbons that do not intersect, determined by the side directions.…

GoV 2 : Viruses and quasicrystals
If you look around for mathematical theories of the structure of viruses, you quickly end up with the work of Raidun Twarock and her group at the University of York. We’ve seen her proposal to extend the CasparKlug classification of viruses. Her novel idea to distribute proteins on the viral capsid along Penroselike tilings shouldn’t…