%0 Journal Article %T Maps admitting trialities but not dualities %A Gareth A. Jones %A Andrew Poulton %J Mathematics %D 2009 %I arXiv %X We use group theory to construct infinite families of maps on surfaces which are invariant under Wilson's map operations of order 3 but not under the operations of order 2, such as duality and Petrie duality. %U http://arxiv.org/abs/0911.2672v1