Let G(d,n) be the Grassmannian parametrizing d-dimensional linear subspaces in an n-dimensional vector space V. It is a projective scheme embedded in P^N for N = (n,d) − 1 via its Plücker embedding. Let L be a distributive lattice. Then one can form the Hibi variety, which is a binomial scheme defined by certain relations coming from the lattice L. It is well-known that the Grassmannian G(d, n) degenerates to a Hibi variety associated to a certain lattice. The ideal of the Hibi variety has a nice initial ideal such that its initial complex is isomorphic to K := ∆eq ∗ ∆d, where ∆eq is a simplicial sphere and ∆d is a d-simplex. This implies that the Hibi variety degenerates to a Stanley-Reisner scheme P(K). When d = 2, ∆eq is the dual associahedron, and it is known that in this case P(K) is unobstructed. The first example where P(K) is obstructed is for d = 3, n = 6, which will be the topic of this thesis.