Simon's shellable but not vertex decomposable example

Description
Simon's example of a 2-dim simplicial complex which is shellable but not vertex decomposable.
Appears in the appendix of Simon's 1994 paper. With 6 vertices and 10 facets.
Datum
simon2.dat
Some table
vertex decomposable?no
extendably shellable?no
shellable?yes
constructible?yes
Cohen-Macaulay?yes
partitionable?yes
topologycontractible
f-vector(1,6,15,10)
h-vector(1,3,6,0)
made bySimon
References
R.S.Simon, Combinatorial properties of "Cleanness", J. Algebra 167 (1994), 361-388.
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