The notion of Eulerian lattice generalizes the notion of face lattice of a convex polytope.

(Bruggesse-Mani): The boundary complex of a convex polytope is shellable.

(Björner-Wachs): A poset is said to be shellable if its order complex is shellable. A bounded poset is shellable if and only if its proper part is shellable.

(Wachs): The order complex of the face poset of a simplicial complex is its barycentric subdivision.

*Pre-question*: Is the shellability kept by taking the barycentric subdivision?

If so, the face lattice of a convex polytope is shellable. This leads to:

**Question**: Is an Eulerian lattice shellable?