Input: | Lattice L |
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Output: | "Yes" if L is isomorphic to the face lattice
of a simplicial polytope, "No" otherwise |

Status (general): | NP-hard |
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Status (fixed dim.): | Open |

As for Problem 30, L is
ranked, atomic, and coatomic if the answer is "Yes." In this
case, the dimension d of any matched polytope is
rank L-1.
As for general polytopes (Problem 30),
this problem is polynomial time solvable in dimension The problem is The following question is interesting in connection with
Problem 17 (see also the notes there): Given an
(abstract) graph |

Related problems: | 17, 30 |
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