  The combinatorial structure of Pachner moves in four dimensions is analyzed
in the case of a distinguished move of the type (3,3) and few examples of
solutions are reviewed. In particular, solutions associated to Pontryagin
self-dual locally compact abelian groups are characterized with remarkable
symmetry properties which, in the case of finite abelian groups, give rise to a
simple model of combinatorial TQFT with corners in four dimensions.
