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Orientable self-embeddings of Steiner triple systems of order 15

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It is shown that for 78 of the 80 isomorphism classes of Steiner triple systems of order 15 it is possible to find a face 2-colourable triangulation of the complete graph K_{15} in an orientable surface in which the colour classes both form representatives of the specified isomorphism class. For one of the two remaining isomorphism classes it is proved that this is not possible. We also discuss the remaining open case.

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