Every large 3-uniform hypergraph whose vertex count is a multiple of five and whose minimum codegree is at least 2n/5 admits a perfect tiling by the generalized triangle, and this threshold is best possible.
Bollob\' a s , Three-graphs without two triples whose symmetric difference is contained in a third , Discrete Mathematics 8 (1974), 21--24
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Perfect tilings of 3-graphs with the generalised triangle
Every large 3-uniform hypergraph whose vertex count is a multiple of five and whose minimum codegree is at least 2n/5 admits a perfect tiling by the generalized triangle, and this threshold is best possible.