  We show that the self-assembly of a diverse collection of building blocks can
be understood within a common physical framework. These building blocks, which
form periodic honeycomb networks and nonperiodic variants thereof, range in
size from atoms to micron-scale polymers, and interact through mechanisms as
different as hydrogen bonds and covalent forces. A combination of statistical
mechanics and quantum mechanics shows that one can capture the physics that
governs assembly of these networks by resolving only the geometry and strength
of building block interactions. The resulting framework reproduces a broad
range of phenomena seen experimentally, including periodic and nonperiodic
networks in thermal equilibrium, and nonperiodic supercooled and glassy
networks away from equilibrium. Our results show how simple `design criteria'
control assembly of a wide variety of networks, and suggest that kinetic
trapping can be a useful way of making functional assemblies.
