Foams appear ubiquitously in many fields of science and technology. However, applications to photonics have not been possible because until now, foam-based 3D heterostructures with substantial complete photonic band gaps have not been identified. Here we provide explicit examples based on the edges of dry-crystalline foams, including the famous Weaire–Phelan foam. More generally, foam networks based on Frank–Kasper phases offer new, promising approaches to the rapid self-organization of large photonic networks. Moreover, foams are excellent candidates for designer materials with versatile multifunctional characteristics.