Upper bound of a band complex

The band structure for a crystal generally consists of connected components in energy-momentum space, known as complexes. Here, we explore fundamental aspect regarding the maximal number bands that can be accommodated single complex. We show that, principle, complex have no finite upper bound certain space groups. This means infinitely many entangle together, forming pattern stable against symmetry-preserving perturbations. is demonstrated by our developed inductive construction procedure, through which given always grown into larger one gluing basic building block to it. As by-product, demonstrate existence arbitrarily large accordion-type structures containing ${N}_{C}=4n$ bands, with $n\ensuremath{\in}\mathbb{N}$.