The GIT boundary of quintic threefolds consists of 38 components whose general polystable representatives have minimal exponent 1 and form a connected codimension-one adjacency graph with 184 edges and diameter 4.
Lakhani, The GIT Compactification of Quintic Threefolds, arXiv:1010.3803 [math.AG]
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The GIT Boundary of Quintic Threefolds (Announcement of Results)
The GIT boundary of quintic threefolds consists of 38 components whose general polystable representatives have minimal exponent 1 and form a connected codimension-one adjacency graph with 184 edges and diameter 4.