Ziegler's 3-ball

Description

Ziegler's 1998 paper showed a very small non-shellable 3-ball which is even smaller thatn Gru"nbaum's ball. This amazing example has only 10 vertices and 21 facets. (Believed to be the smallest.)

Properties

This is known to be constructible.

Datum

ziegler.dat

Some table

vertex decomposable?	no
extendably shellable?	no
shellable?	no
constructible?	yes
Cohen-Macaulay?	yes
partitionable?	yes
topology	3-ball
f-vector	(1,10,38,50,21)
h-vector	(1,6,14,0,0)
made by	Ziegler

References

G.M.Ziegler, Shelling polyhedral 3-balls and 4-polytopes, Discrete Comput. Geom. 19 (1998), 159-174.