  A Hamilton decomposition of a graph is a partitioning of its edge set into
disjoint spanning cycles. The existence of such decompositions is known for all
hypercubes of even dimension $2n$. We give a decomposition for the case $n =
2^a3^b$ that is highly symmetric in the sense that every cycle can be derived
from every other cycle just by permuting the axes. We conjecture that a similar
decomposition exists for every n.
