Rudin's 3-ball

Description

Rudin showed in her 1958 paper that we can triangulate a 3-tetrahedron by introducing 10 vertices on the boundary in such a way that the resulting triangulation is not shellable. This triangulation has 14 vertices and 41 facets. An interesting fact is that all the vertices can be perturbed into a position that the 3-ball is strictly convex, that is, this achieve a nonshellable 3-ball with a convex realization.

Properties

Chillingworth(1967)'s theorem shows this triangulation is simplicially collapsible. Also this example is known to be constructible.

Datum

rudin.dat

Some table

vertex decomposable?	no
extendably shellable?	no
shellable?	no
constructible?	yes
Cohen-Macaulay?	yes
partitionable?	yes
topology	3-ball
f-vector	(1,14,66,94,41)
h-vector	(1,10,30,0,0)
made by	Rudin

References

M.E.Rudin, An unshellable triangulation of a tetrahedron, Bulltin Amer. Math. Soc. 64 (1958), 90-91.

D.R.J. Chillingworth, Collapsing three-dimensional convex polyhedra, Math. Proc. Camb. Phil. Soc. 63 (1967), 353-357. (Errata in Math. Proc. Camb. Phil. Soc. 88 (1980), 307-310.)