Non-extendably shellable example

Description

The vertices with the same labling are identified.

Properties

Shellable but not extendably shellable. That this example is contractible and that {1,3} is the only boundary part imply that every shelling should end by {1,3,4}. Thus not extendably shellable. (Partial shellings started from {1,3,4} can not be completed.)

Datum

nonextend.dat

Some table

vertex decomposable?	no
extendably shellable?	no
shellable?	yes
constructible?	yes
Cohen-Macaulay?	yes
partitionable?	yes
topology	contractible
f-vector	(1,7,19,13)
h-vector	(1,4,8,0)
made by	Hachimori

References

M.Hachimori, Combinatorics of constructible complexes, PhD thesis.