Polycontinuous morphologies and interwoven helical networks

Department of Applied Mathematics, Research School of Physical Sciences Australian National University, Canberra, ACT 0200, Australia

Received: 25 October 1999
Accepted: 27 January 2000

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 , four and eight 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.