Gru"nbaum's 3-ball

Description

Gru"nbaum made a very small example of a non-shellable triangulation of a 3-ball and achieved it with 14 vertices and 29 facets. This is smaller than Rudin's ball. (This seems not have a convex realization. But this has a (nonconvex) realization in 3-dim space.)

Properties

This example is known to be constructible

Datum

gruenbaum.dat

Some table

vertex decomposable?	no
extendably shellable?	no
shellable?	no
constructible?	yes
Cohen-Macaulay?	yes
partitionable?	yes
topology	3-ball
f-vector	(1,14,54,70,29)
h-vector	(1,10,18,0,0)
made by	Grunbaum

References

G.Danaraj and V.Klee, Which spheres are shellable?, Annals of Discrete Mathematics 2 (1978), 33-52.