We show that any –dimensional nonnegatively curved Alexandrov space with the maximal possible number of extremal points is isometric to a quotient space of by an action of a crystallographic group. We describe all such actions.
"Alexandrov spaces with maximal number of extremal points." Geom. Topol. 19 (3) 1493 - 1521, 2015. https://doi.org/10.2140/gt.2015.19.1493