  We construct a smoothing of a particular normal crossing surface, which dual
complex is a duncehat, thus obtaining an example of a surface degeneration with
non-collapsible, contractible dual complex. The general fiber of this family
has $h^{1,0} = h^{2,0} = 0$ and $h^{1,1}=9$, we conjecture that it is in the
deformation class of the Barlow surface. This text is a complete rewrite of
author's previous work [14].
