The poetry of Steiner systems

A Steiner triple system consists of a set S (such as the set of seven letters {A, E, H, R, T, W, Y}) together with a set of 3-element subsets of S called blocks (such as {YEA, WHY, TRY, HER, RAW, WET, HAT}). These blocks are represented in the diagram above by six straight lines and a circle. The property that makes this a Steiner system is that any pai…