Abstract
We prove that every five-dimensional polytope has a two-dimensional face which is a triangle or a quadrilateral. We state and discuss the following conjecture: For every integer k≥1 there is an integer f(k) such that every d-polytope, d≥f(k), has a k-dimensional face which is either a simplex or combinatorially isomorphic to the k-dimensional cube. We give some related results concerning facet-forming polytopes and tilings. For example, sharpening a result of Schulte [25] we prove that there is no face to face tiling of ℝ5 with crosspolytopes.
Original language | English |
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Pages (from-to) | 271-280 |
Number of pages | 10 |
Journal | Combinatorica |
Volume | 10 |
Issue number | 3 |
DOIs | |
State | Published - Sep 1990 |
Keywords
- AMS subject classification (1980): 52A25, 52A20