Geodesic
Minimal bounded lattices with an antitone involution the complemented elements of which do not form a sublattice
Discussiones Mathematicae. General Algebra and Applications, Tome 28 (2008) no. 2, pp. 251-259.

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Bounded lattices with an antitone involution the complemented elements of which do not form a sublattice must contain two complemented elements such that not both their join and their meet are complemented. We distinguish (up to symmetry) eight cases and in each of these cases we present such a lattice of minimal cardinality.
Keywords: bounded lattice, antitone involution, complemented element 
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Chajda, Ivan; Länger, Helmut. Minimal bounded lattices with an antitone involution the complemented elements of which do not form a sublattice. Discussiones Mathematicae. General Algebra and Applications, Tome 28 (2008) no. 2, pp. 251-259. http://geodesic.mathdoc.fr/item/DMGAA_2008_28_2_a8/

[1] G. Birkhoff, Lattice Theory, AMS, Providence, R. I., 1979.

[2] I. Chajda and H. Länger, Bounded lattices with antitone involution the complemented elements of which form a sublattice, J. Algebra Discrete Structures 6 (2008), 13-22.

[3] G. Grätzer, General Lattice Theory, Birkhäuser, Basel 1998.