TITLE: Uniquely complemented lattice that is non-modular
QUESTION [8 upvotes]: I'm looking for an explicit example of a uniquely complemented lattice that is non-modular, since neither of the two non-modular lattices described here at wikipedia have this property.
Thanks.

REPLY [8 votes]: We know that uniquely complemented lattices that are non-modular exist. This follows from the celebrated result by Dilworth (pdf). As far as I know, we do not know how to exhibit a concrete example, all the known constructions use some sort of complicated colimit. See the
Graetzers paper in Notices (pdf) for a general overview of results concerning unique complementation and much more.