A web of confocal parabolas in a grid of hexagons (Q6174571)

In this paper, the authors consider regular hexagons erected upon the sides of a triangle. The construction is analogous to the construction in the well-known Napoleon theorem which deals with equilateral triangles. It can be extended iteratively, forming a tiling of the plane consisting of regular hexagons and flank triangles. The authors show that the vertices of the hexagons are interwoven by a web of confocal parabolas with three distinct foci.