  We show that a fixed set of woven defect lines in a nematic liquid crystal
supports a set of non-singular topological states which can be mapped on to
recurrent stable configurations in the Abelian sandpile model or chip-firing
game. The physical correspondence between local Skyrmion flux and sandpile
height is made between the two models. Using a toy model of the elastic energy,
we examine the structure of energy minima as a function of topological class
and show that the system admits domain wall Skyrmion solitons.
