Experimental advances in the synthesis of colloids and nanoparticles with control over their shape and interactions [1,2] have opened an avenue for the design of new materials with desired functionalities. To leverage the full potential of this approach, it is necessary to decipher the relation between the particles’ interactions and the ordered structures that they can form. In this talk, we will show how to rationally design a model system to obtain a given target structure, focusing on icosahedral quasicrystals (IQCs). These are materials that are ordered but lack periodicity in any direction of space. In nature, they have been observed in many metallic alloys, but, so far, never in non-metallic or one-component systems [3,4]. We demonstrate that IQCs can be engineered by using model particles with bonds that mimic the local environments found in the target IQC [5]. We hypothesize that the designed models might be experimentally realizable in light of the impressive advances in the design of DNA origamis [6] and proteins [7]. If the time allows, we will also discuss the possibility of using a similar approach to assemble axial quasicrystals (which are aperiodic in two dimensions, but periodic in the third one).

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[4] H. Takakura, et al., Nat. Mater. 6 (2007) 58.
[5] E. G. Noya, C. K. Wong, P. Llombart, J. P. K. Doye, Nature 596 (2021) 367; E.G. Noya, J.P.K. Doye, ACS Nano 19 (2025) 13714.
[6] Y. Tian et al., Nat. Mater. 19 (2020) 789.
[7] Li, et al., Nat. Mater. 22 (2023) 1556.

Acknowledgements. Financial support from Agencia Estatal de Investigación, Grant No PID2023-151751NB-I00 is gratefully acknowledged.