Geometrical frustration and defects in condensed matter systems

The concept of geometrical frustration is recalled, in particular in the case of frustrated icosahedral order. The curved space approach allows one to relax the frustration at the price of curving the underlying space. Topological defects are then introduced to produce a realistic structure in R3. In this paper we focus on the description of two types of large cell crystalline structures with frustrated order, the metallic Frank–Kasper alloys and the cholesteric blue phases. Both structures can be described as a periodic array of disclination line defects threading a medium with (slightly deformed) local and medium range order.