An 8-dimensional 0/1-polytope found by Thomas Christof that has 38 vertices and 1675 facets.
DIM 8 VERTICES 1 0 1 1 1 1 0 1 0 1 0 1 0 0 1 0 1 1 1 1 0 1 0 1 1 0 0 1 1 0 1 0 1 0 1 1 1 0 0 1 1 0 0 1 1 1 1 0 1 1 0 0 0 0 1 1 1 1 0 1 1 0 1 1 0 0 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 1 1 1 1 1 1 1 0 0 1 0 1 0 1 1 0 0 0 0 1 1 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 0 1 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 1 0 0 0 1 1 1 0 1 1 1 0 0 0 0 1 0 1 1 1 1 0 1 0 1 0 1 0 0 1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 1 1 0 0 1 1 1 1 0 1 1 1 1 0 1 1 0 0 1 0 1 0 1 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 0 1 1 1 1 1 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 1 0 0 0 1 0 1 FACETS 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 -1 0 0 1 1 1 0 1 0 -1 0 0 1 1 1 -1 1 0 0 0 0 1 1 1 -1 0 0 1 0 0 1 1 0 1 0 1 -1 0 0 1 1 0 -1 1 0 0 1 0 1 1 -1 1 0 1 0 0 0 1 1 -1 1 0 0 1 0 0 1 0 1 1 1 0 -1 0 0 1 0 1 1 0 0 -1 1 0 1 0 1 -1 1 0 1 0 0 1 0 1 -1 0 1 1 0 0 1 0 0 1 0 1 -1 1 0 1 0 0 0 1 1 -1 1 0 1 0 -1 1 0 1 0 1 0 1 0 -1 1 0 0 1 1 0 1 -1 1 1 0 0 0 1 0 1 -1 1 0 1 1 0 0 0 1 -1 1 0 0 1 1 0 0 1 -1 1 0 0 1 0 1 0 1 -1 0 1 1 0 0 1 0 1 -1 0 1 0 1 0 1 0 1 -1 0 1 0 0 1 1 0 0 1 1 1 1 0 -1 0 0 0 1 1 1 0 1 -1 0 0 0 1 1 0 1 0 -1 1 0 0 1 0 1 0 1 -1 1 0 0 1 0 0 1 1 -1 1 0 0 1 -1 1 1 1 0 0 0 0 1 -1 1 1 0 1 0 0 0 1 -1 1 0 1 1 0 0 0 1 -1 1 0 1 0 1 0 0 0 -1 1 1 1 0 1 0 0 0 -1 1 1 0 1 1 0 0 0 -1 1 0 1 1 1 0 0 -1 1 1 0 0 1 1 0 0 -1 1 0 1 0 1 1 0 0 -1 1 0 0 1 1 1 0 0 -1 0 1 1 0 1 1 0 0 -1 0 1 0 1 1 1 0 -1 1 1 1 1 0 0 0 0 -1 1 1 1 0 1 0 0 0 -1 1 1 1 0 0 1 0 0 -1 1 0 1 1 1 0 0 0 -1 1 0 1 1 0 1 0 0 -1 1 0 1 1 0 0 1 0 -1 1 0 1 0 1 1 0 0 -1 1 0 1 0 1 0 1 0 -1 0 1 1 0 0 1 1 0 -1 0 0 1 1 0 1 1 0 -1 0 0 1 0 1 1 1 0 1 1 0 -1 1 1 1 0 0 1 1 -1 0 1 1 1 0 0 1 -2 1 1 0 1 1 1 0 1 1 2 1 1 0 -2 0 0 0 2 1 1 1 1 -2 0 0 2 -1 1 1 1 0 -1 1 0 2 -1 0 1 1 1 -1 1 0 1 1 1 -1 2 0 -1 1 0 1 1 -1 1 0 2 -1 1 0 1 0 1 -1 2 1 -1 1 0 1 0 -1 1 1 2 -1 1 0 1 -1 2 -1 1 1 1 0 0 -1 2 1 1 1 1 -1 0 0 -1 2 0 1 1 1 -1 1 0 -1 1 -1 2 1 1 1 0 0 -1 1 -1 2 1 1 0 1 0 -1 0 -1 2 1 1 1 1 0 2 1 1 -2 1 1 1 0 0 2 1 1 -2 1 0 1 1 0 1 2 -2 1 1 1 1 0 0 1 1 -2 1 1 0 2 1 0 2 -1 1 0 1 0 -1 2 0 1 0 1 -1 2 0 -1 2 0 1 -1 2 -1 1 2 0 0 0 -1 0 -1 2 2 0 1 1 0 2 1 2 -2 1 0 1 0 0 2 1 1 -2 2 0 0 1 0 2 -2 1 1 0 1 0 2 0 1 2 1 2 0 1 -2 0 0 1 2 -2 2 0 1 1 0 0 1 1 0 2 0 2 -2 1 0 1 0 -2 2 0 1 1 2 0 1 -2 2 0 0 2 1 1 0 1 -2 1 2 0 0 1 2 0 1 -2 0 2 1 0 1 2 0 1 -2 0 2 0 1 1 2 0 0 2 -2 2 1 1 1 0 0 0 1 -2 2 0 2 1 1 0 0 0 -2 2 1 1 1 2 0 0 -2 1 1 1 0 2 2 0 -2 2 1 2 1 1 0 0 0 -2 2 1 2 1 0 1 0 0 -2 2 1 2 0 1 1 0 0 -2 2 0 2 1 1 1 0 0 -2 2 0 2 1 1 0 1 0 -2 1 0 2 2 0 1 1 0 -2 1 0 2 0 2 1 1 0 1 1 0 -1 2 1 -1 2 0 1 1 -1 0 1 2 -1 2 0 -1 2 1 1 2 0 -1 1 0 2 1 -1 2 0 2 -1 0 0 2 0 -1 2 0 2 -1 1 0 2 -1 2 1 0 0 -1 2 0 2 -1 2 -1 0 2 1 0 0 2 -1 1 0 2 2 -1 0 0 0 2 -1 1 0 2 -1 2 0 0 1 -1 2 2 2 -1 0 0 -1 2 2 1 0 2 -1 0 0 -1 2 0 1 2 2 -1 0 0 -1 2 0 1 0 2 -1 2 0 -1 1 -1 2 2 2 0 0 0 -1 1 -1 2 2 0 2 0 0 -1 1 -1 2 0 2 2 0 0 -1 0 -1 2 0 2 2 1 0 -1 -1 2 1 0 0 2 2 0 -1 -1 0 1 2 0 2 2 0 -1 -1 0 1 0 2 2 2 0 2 1 2 1 2 1 -3 0 0 2 -3 1 2 0 1 1 2 0 1 2 1 2 1 2 -3 0 0 1 -3 1 2 0 1 2 2 0 2 -1 -1 2 1 2 -1 2 0 -1 -1 -1 2 1 2 2 2 0 1 1 -1 1 1 3 -2 2 0 1 1 -2 1 1 3 -1 2 0 1 -2 3 -1 2 1 1 1 0 3 -1 2 1 1 0 -2 2 0 3 -1 1 0 2 2 -2 1 0 3 -1 0 1 2 2 -2 1 0 3 -2 2 1 1 0 -1 2 0 3 -2 2 0 1 1 -1 2 0 3 -2 1 1 2 0 -1 2 0 2 1 1 -2 3 0 -1 2 0 2 1 -1 2 0 3 -2 1 0 2 1 -2 2 0 3 -1 1 0 2 0 1 -1 3 1 -2 2 0 2 0 -1 2 1 3 -2 1 0 2 -1 3 -2 1 2 1 0 0 2 -2 3 -1 1 2 1 0 0 1 1 2 -1 3 0 -2 2 0 0 2 -1 1 1 3 -2 2 0 0 1 -2 2 2 3 -1 1 0 -1 3 2 1 1 2 -2 0 0 -1 3 1 1 2 2 -2 0 0 -1 3 0 1 2 2 -2 1 0 -1 3 0 1 1 2 -2 2 0 -1 1 -2 3 2 2 0 1 0 -1 0 -2 3 2 1 1 2 0 3 1 2 -3 2 1 1 0 0 3 1 2 -3 2 0 1 1 0 3 1 2 -3 1 1 2 0 0 1 3 -3 2 1 2 1 0 0 1 3 -3 2 1 1 2 0 0 1 2 1 3 0 2 -3 1 0 -3 2 1 3 2 0 1 1 0 -3 2 1 3 0 2 1 1 0 2 -1 2 -1 2 3 -1 0 0 -1 -1 -1 2 3 0 2 2 0 -3 3 1 3 1 1 1 0 0 3 -1 1 2 3 1 -2 0 0 3 -2 2 1 0 1 -1 3 0 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