Polycontinuous morphologies and interwoven helical networks

We describe a construction procedure for polycontinuous structures, giving generalisations of bicontinuous morphologies to more than two equivalent, c ontinuous and interwoven sub-volumes. The construction gives helical windin gs of disjoint graphs on triply periodic hyperbolic surfaces, whose univers al cover in the hyperbolic plane consists of packed, parallel trees. The si mplest tri-, quadra- and octa-continuous morphologies consist of three (8, 3) - c, four (10, 3) - a and eight (10, 3) - ct interwoven networks, respec tively. The quadra- and octa-continuous cases are chiral. A novel chiral bi continuous structure is also derived, closely related to the well-known cub ic gyroid mesophase.