Nanoparticles and colloids functionalized by four single strands of DNA can be thought of as designed analogs to tetrahedral network-forming atoms and molecules, with a difference that the attached DNA strands allow for control of the length scale of bonding relative to the core size. We explore the behavior of an experimentally realized model for nanoparticles functionalized by four single strands of DNA (a tetramer), and show that this single-component model exhibits a rich phase diagram with at least three critical points and four thermodynamically distinct amorphous phases. We demonstrate that the additional critical points are part of the Ising universality class, like the ordinary liquid-gas critical point. The dense phases consist of a hierarchy of interpenetrating networks, reminiscent of a woven cloth. Thus, bonding specificity of DNA provides an effective route to generate new nano-networked materials with polyamorphic behavior. The concept of network interpenetration helps to explain the generation of multiple liquid phases in single-component systems, suggested to occur in some atomic and molecular network-forming fluids, including water and silica. DNA functionalization ͉ nanoparticles ͉ self-assembly ͉ polyamorphism ͉ nanotechnology T echnological developments are creating a wide variety of building blocks that play the role of ''functionalized atoms'' for designed materials (1, 2). Borrowing ideas from biological specificity (3-6), it is now possible to control bonding between engineered building blocks in a selective way, moving in the direction of an effective synthetic bottom-up strategy for selfassembly. The complementary binding of base pairs, combined with the ability to directly control the base sequence, makes DNA an ideal candidate for the development of network-based, nanostructured materials (5-8). A variety of experiments (7)(8)(9)(10)(11)(12)(13)(14)(15) have demonstrated the possibility to realize nanostructured, DNAbased materials, including ordered crystal structures (9, 10).By grafting short single strands of DNA to core particles, the core can act as a ''node'' of a complex network formed when single strands combine into dsDNA. Longer linking ''arms'' may be achieved by using a double-stranded spacer near the core nanoparticle (9, 10). With an intelligent choice of the core, it is possible to control the number of attached strands and thus the nearest-neighbor coordination of the functionalized nanoparticle, providing a direct route to study materials where the bonding coordination is much less than that of spherically symmetric molecules (16). In such limited coordination systems, the general features of network formation are expected to be observed.By functionalizing the central core with four DNA strands, we expect to generate an engineered analog of tetrahedral networkforming atoms or molecules, in which the bonding contribution to the interparticle interaction energy can be tuned by modulating the length L of the DNA strand, as well as the chemical properties of the solvent....