Abstract
We describe a construction procedure for polycontinuous structures, giving generalisations of bicontinuous morphologies to more than two equivalent, continuous and interwoven sub-volumes. The construction gives helical windings of disjoint graphs on triply periodic hyperbolic surfaces, whose universal cover in the hyperbolic plane consists of packed, parallel trees. The simplest tri-, quadra- and octa-continuous morphologies consist of three (8,3) − c, four (10,3) − a and eight (10,3) − a interwoven networks, respectively. The quadra- and octa-continuous cases are chiral. A novel chiral bicontinuous structure is also derived, closely related to the well-known cubic gyroid mesophase.