The construction of honeycombs
from overlapping Y pieces may be generalised to include knot crossing pieces. This means working with knotted trivalent graphs for which Kuperberg's
spider rules are useful. For example, in the 2x2 case there is the operation
and the resolution of one crossing into a >-< diagram appears on the right hand side. There is also a dual relation arising from the opposite crossing.
Thanks to Nigel
for this link
to a classic paper by J. C. Maxwell
involving honeycomb diagrams. In a way, M theory has returned us to this aether, but induced backgrounds
in measurement geometry are imposed by the observer and by no means a casual aether in the traditional sense.