A challenge of molecular self-assembly is to understand how to design particles that self-assemble into a desired structure and not any of a potentially large number of undesired structures. Here we use simulation to show that a strategy of minimal positive design allows the self-assembly of networks equivalent to the 8 semiregular Archimedean tilings of the plane, structures not previously realized in simulation. This strategy consists of identifying the fewest distinct types of interparticle interaction that appear in the desired structure, and does not require enumeration of the many possible undesired structures. The resulting particles, which self-assemble into the desired networks, possess DNA-like selectivity of their interactions. Assembly of certain molecular networks may therefore require such selectivity.Molecular self-assembly is the spontaneous organization of molecules or other small particles into structures [1][2][3][4][5][6][7][8][9][10]. Despite many successes in the laboratory we lack complete understanding of how to design particles that will self-assemble into a desired structure: sometimes the outcome of self-assembly is an undesired structure, which might be metastable or kinetically trapped [11]. Simulation can help us understand how particle design influences the process and outcome of self-assembly [12][13][14][15][16][17]. Ideas derived from such studies include the notion of positive and negative design, used by Doye, Louis and Vendruscolo [12] to describe the design of particles to promote a desired structure or to suppress undesired structures. We show here that a particular type of positive design, which we shall call minimal positive design, allows the self-assembly of network structures equivalent to the Archimedean tilings of the plane. The concept is simple to implement: we drew pictures of the desired structures and labeled the interparticle interactions that arise, and then (on the computer) made particles with those interactions and no others. Those particles self-assembled, under a simple cooling protocol, into the desired structures, which had not previously been realized in simulation [18]. The field of DNA nanotechnology makes widespread use of the principle of chemical selectivity [19][20][21][22], allowing, for instance, self-assembly of structures in which particles are of many distinct types [7,23,24]. Here we show that chemically selective interactions are also necessary to assemble certain complex single-component structures, which a priori do not appear to require this capability. By formalizing the idea of minimal positive design we hope to provide a way of thinking about chemical selectivity and its role in self-assembly.We illustrate the concept of minimal positive design by considering the self-assembly of networks equivalent to tilings of the plane [25,26]. Such networks are complex geometrically, and so pose a challenge for design, and their experimental realizations, via the self-assembly of real molecules at surfaces, have useful properties [27- * swhitela...