Example of a uniquely complemented lattice?

Question

I'm approaching lattices. I have understood the definition of a Lattice, a Complete Lattice and a Bounded Lattice.
Theoretically, even the definition of a complemented lattice doesn't seem difficult, but I couldn't get any satisfying examples.
In fact, every time I searched for it, I only got pictures of graphs with letters on vertices and a $0$ and a $1$ on the remaining vertices.
I'd love to have a number set example if it's possible, or a non-strictly mathematical (real-life set) example, or just something that is really intuitive.

Answer 1

If you're interested in uniquely complemented lattices, then

• In the distributive case (all the distributive complemented lattices), they're Boolean, that is, they are the lattice reducts of Boolean algebras (so, in the finite case, which might be what you're interested in, they have the shape $\mathbf 2^n$, for some natural number $n$);
• In the non-distributive case, these seem very elusive creatures, although they exist (but they are infinite). See the answer to this question with links to related papers. To emphasize how elusive these seem to be, note this sentence in the linked paper by Grätzer (end of part 2):

  It is interesting how little we know about a subject on which we have published so many papers.
  Ask any question and probably we do not know the answer.

Answer 2

According to this Wolfram entry, any Boolean algebra is a uniquely complemented lattice.

http://mathworld.wolfram.com/UniquelyComplementedLattice.html