Abstract
What is the minimal closed cone containing all f-vectors of cubical d-polytopes? We construct cubical polytopes showing that this cone, expressed in the cubical g-vector coordinates, contains the nonnegative g-orthant, thus verifying one direction of the Cubical Generalized Lower Bound Conjecture of Babson, Billera, and Chan. Our polytopes also show that a natural cubical analogue of the simplicial Generalized Lower Bound Theorem does not hold.
Original language | English |
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Pages (from-to) | 1851-1866 |
Number of pages | 16 |
Journal | Proceedings of the American Mathematical Society |
Volume | 147 |
Issue number | 5 |
DOIs | |
State | Published - May 2019 |
Bibliographical note
Publisher Copyright:© 2019 American Mathematical Society.