  In 2009 Chmutov introduced the idea of partial duality for embeddings of
graphs in surfaces. We discuss some alternative descriptions of partial
duality, which demonstrate the symmetry between vertices and faces. One is in
terms of band decompositions, and the other is in terms of the gem
(graph-encoded map) representation of an embedding. We then use these to
investigate when a partial dual is a closed 2-cell embedding, in which every
face is bounded by a cycle in the graph. We obtain a necessary and sufficient
condition for a partial dual to be closed 2-cell, and also a sufficient
condition for no partial dual to be closed 2-cell.
