Isogonal non-crystallographic periodic graphs based on knotted sodalite cages

This work considers non-crystallographic periodic nets obtained from multiple identical copies of an underlying crystallographic net by adding or flipping edges so that the result is connected. Such a structure is called a `ladder' net here because the 1-periodic net shaped like an ordinary (infinite) ladder is a particularly simple example. It is shown how ladder nets with no added edges between layers can be generated from tangled polyhedra. These are simply related to the zeolite nets SOD, LTA and FAU. They are analyzed using new extensions of algorithms in the program Systre that allow unambiguous identification of locally stable ladder nets.