Dr. Arsalan Wares’ letter this month is beautiful, as always, but sadly recounts a tale of honeycomb horror. The diagram in Figure 3 depicts a portion of a tiling of the plane by regular hexagonal tiles. All line segments shown have endpoints at the vertices of the tiling. Dr. Wares woke up one morning to find the region
of the tiling shown in pink… simply gone. Perhaps it was removed in the night by a mysterious tiling marauder with a love of sixfold symmetry?
In any case, Dr. Wares wonders: what fraction of the area of each of the six partially-removed tiles is missing?