This story begins in Nick Lord's workshop session at the Joined Up Mathematics conference at Keele in April 2008. He had decided to talk about Figure 1 and the results concerning it featured in [1]. He was also having an interesting e-mail exchange with Douglas Rogers, who pointed out that iterating such constructions twice produced a triangle homothetic to the original. The exchange focused on the analogous iterated Vecten configuration which John Mason recently discussed in [2]; but Nick could not see a similarly quick argument for the results in [1], which he thus set as a ‘homework problem’ for the workshop participants.