Constructible but not shellable example

Description

Identify the vertices with the same label.

Properties

Non-shellability is a consequence of the fact that this example is contractible but has no boundary. Constructibility can be easily checked. In particular, it should be noted that having no boundary and to be contractible do not imply non-constructibility.

This example, inspired from the nonextendable example of Moriyama & Takeuchi, is smaller than c-ns.dat and c-ns2.dat.

Datum

c-ns3.dat

Some table

vertex decomposable?	?
extendably shellable?	no
shellable?	no
constructible?	yes
Cohen-Macaulay?	yes
partitionable?	yes
topology	contractible
f-vector	(1,10,31,22)
h-vector	(1,7,14,0)
made by	Hachimori

References

Not published yet.