Identical twin Steiner triple systems

Grannell, M. J. and Lovegrove, G. J. (2016). Identical twin Steiner triple systems. The Australasian Journal of Combinatorics, 66(1) pp. 130–141.



Two Steiner triple systems, each containing precisely one Pasch configuration which, when traded, switches one system to the other, are called twin Steiner triple systems. If the two systems are isomorphic the systems are called identical twins. Hitherto, identical twins were only known for orders 21, 27 and 33. In this paper we construct infinite families of identical twin Steiner triple systems.

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