Construction techniques for cubical complexes, odd cubical 4-polytopes, and prescribed dual manifolds
| dc.creator | Schwartz, Alexander | |
| dc.creator | Ziegler, Guenter M. | |
| dc.date | 2003-10-17 | |
| dc.date | 2004-01-02 | |
| dc.date.accessioned | 2026-07-07T05:02:01Z | |
| dc.date.available | 2026-07-07T05:02:01Z | |
| dc.description | We provide a number of new construction techniques for cubical complexes and cubical polytopes, and thus for cubifications (hexahedral mesh generation). As an application we obtain an instance of a cubical 4-polytope that has a non-orientable dual manifold (a Klein bottle). This confirms an existence conjecture of Hetyei (1995). More systematically, we prove that every normal crossing codimension one immersion of a compact 2-manifold into R^3 PL-equivalent to a dual manifold immersion of a cubical 4-polytope. As an instance we obtain a cubical 4-polytope with a cubation of Boy's surface as a dual manifold immersion, and with an odd number of facets. Our explicit example has 17 718 vertices and 16 533 facets. Thus we get a parity changing operation for 3-dimensional cubical complexes (hexa meshes); this solves problems of Eppstein, Thurston, and others. | |
| dc.description | condensed and revised version; 39 pages | |
| dc.identifier | https://arxiv.org/abs/math/0310269 | |
| dc.identifier | http://arxiv.org/abs/math/0310269 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68895 | |
| dc.subject | Combinatorics | |
| dc.subject | 52B12; 52B11; 52B05; 57Q05 | |
| dc.title | Construction techniques for cubical complexes, odd cubical 4-polytopes, and prescribed dual manifolds | |
| dc.type | text |