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 and star polyphiles
  • 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
  • graph theory and net embeddings
  • triply-periodic minimal surfaces and related polycontinuous patterns

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.

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.

More details can be found HERE

The Niels Bohr Institute
Auditorium 2
Ørsted Laboratory Universitetsparken 5 2100 Copenhagen Denmark
Jacob Kirkensgaard (Niels Bohr Institute -
Stephen Hyde (Australian National University)
Kell Mortensen (Niels Bohr Institute)

Jacob Kirkensgaard (