This 5 ECTS point course will explore the geometry and topology of ordered cellular patterns such as foams, bicontinuous and polycontinuous forms and nets found in synthetic and biological materials, including:

mesoporous silicates
metal organic frameworks and coordination polymers
amphiphiles, lipids, star polyphiles forming lyotropic liquid crystals
block copolymers including star miktoarm copolymers

Lectures will emphasise the fundamental structural aspects, with an introduction to the following concepts from modern geometry, crystallography and topology:

two-dimensional symmetries and orbifolds (wallpaper and point groups)
graph theory and net embeddings, knots and entanglement
triply-periodic minimal surfaces and related polycontinuous patterns
material kirigami and origami
2D hyperbolic tilings and their embedding in 3D

No specialised mathematical knowledge is assumed, apart from some elementary familiarity with the shape of space, polyhedra and symmetry. The course will introduce students to unifying structural concepts in a range of ordered multi-phase hard/soft materials. We encourage students with theoretical or experimental backgrounds to attend.

The course will familiarise students with open-source software for construction and characterisation of structures from nets to surfaces. Hands-on tutorials will explore the concepts, via models and software like Kaleidotile, Surface Evolver, Houdini, GAVROG (3dt and Systre), RCSR, EPINET and ESPResSo for molecular simulations.

Stand-alone evening / afternoon lectures will be presented by active material researchers explaining current understanding of mesoporous materials and associated biological assemblies.


The course is free to attend, but all travel, accommodation and meals are at participants own expense. A limited number of participants will be chosen from the applicants.