Wall’s problem asks if a cohomologically 2–dimensional geometric 3–complex is necessarily homotopy equivalent to a geometric 2–complex. We solve part of the problem when the fundamental group is dihedral of order and give a complete solution for the case where it is the dihedral group of order 8.
"The $D(2)$ property for $D_8$." Algebr. Geom. Topol. 7 (1) 517 - 528, 2007. https://doi.org/10.2140/agt.2007.7.517