  A subgraph of the $n$-dimensional hypercube is called 'layered' if it is a
subgraph of a layer of some hypercube. In this paper we show that there exist
subgraphs of the cube of arbitrarily large girth that are not layered. This
answers a question of Axenovich, Martin and Winter. Perhaps surprisingly, these
subgraphs may even be taken to be induced.
