Shelling Polyhedral 3-Balls and 4-Polytopes |
| |
Authors: | G M Ziegler |
| |
Institution: | Department of Mathematics, MA 6-1, Technische Universit?t Berlin, 10623 Berlin, Germany ziegler@math.tu-berlin.de http://www.math.tu-berlin.de/$\sim$ziegler, DE
|
| |
Abstract: | There is a long history of constructions of nonshellable triangulations of three-dimensional (topological) balls. This paper
gives a survey of these constructions, including Furch's 1924 construction using knotted curves, which also appears in Bing's
1962 survey of combinatorial approaches to the Poincaré conjecture, Newman's 1926 explicit example, and M. E. Rudin's 1958
nonshellable triangulation of a tetrahedron with only 14 vertices (all on the boundary) and 41 facets. Here an (extremely simple) new example is presented: a nonshellable simplicial three-dimensional ball with only
10 vertices and 21 facets.
It is further shown that shellings of simplicial 3 -balls and 4 -polytopes can ``get stuck': simplicial 4 -polytopes are not in general ``extendably shellable.' Our constructions imply that a Delaunay triangulation algorithm of
Beichl and Sullivan, which proceeds along a shelling of a Delaunay triangulation, can get stuck in the three-dimensional version:
for example, this may happen if the shelling follows a knotted curve.
Received November 21, 1995, and in revised form September 20, 1996. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|