Hyde, StephenDe Campo, LilianaOguey, Christophe2015-12-101744-683Xhttp://hdl.handle.net/1885/53587We construct simple models to compare ordered tricontinuous patterns that are topologically consistent with the constraints imposed by three-arm star polyphile self-assembly, analogous to steric packing and elastic bending models used to analyse bicontinuous mesophases in amphiphilic assemblies. We find a number of competing low-energy ordered structures, composed of threading of three identical labyrinths, with three-fold infinite branch lines, that are likely to be of comparable energy for polyphile shapes with moderately splayed arms. These patterns are triply-periodic analogues of the hexagonal honeycomb, which is most favoured for unsplayed three-arm polyphile architectures.Keywords: Amphiphilic; Bicontinuous; Branch-line; Elastic bending; Hexagonal honeycomb; Low energies; Mesophases; Ordered structures; Simple model200910.1039/b822814k2016-02-24