Examples by Moriyama and Takeuchi

Moriyama & Takeuchi attempted to enumerate all shellable non-pseudomanifold 2-dim simplicial complexes, and their enumeration found out many interesting examples.
[Shellable but not extendably shellable 2-dim simplicial complexes.] Among these, v6f9-1 and v6f9-2 are the minimum example with this property.

[Shellable but not vertex decomposable 2-dim simplicial complexes]

Among these,
[Extendably shellable but not vertex decomposable 2-dim simplicial complexes]
Some table
vertex decomposableextendably shellable shellablef-vectorh-vectorComments
v6f9-1.dat noyes (1,6,14,9)(1,3,5,0)
v6f9-2.dat noyes (1,6,14,9)(1,3,5,0)
v6f10-1.dat nonoyes (1,6,15,10)(1,3,6,0)
v6f10-2.dat noyes (1,6,15,10)(1,3,6,0)
v6f10-3.dat noyes (1,6,15,10)(1,3,6,0)
v6f10-4.dat noyes (1,6,15,10)(1,3,6,0)
v6f10-5.dat noyes (1,6,15,10)(1,3,6,0)
v6f10-6.dat noyesyes (1,6,15,10)(1,3,6,0)
v6f10-7.dat noyesyes (1,6,15,10)(1,3,6,0)
v6f11-1.dat noyes (1,6,15,11)(1,3,6,1)
v6f11-2.dat noyes (1,6,15,11)(1,3,6,1)
v6f11-3.dat noyes (1,6,15,11)(1,3,6,1) The same as bjorner.dat.
v7f11.dat noyes (1,7,17,11)(1,4,6,0)
v7f12.dat noyes (1,7,18,12)(1,4,7,0)
v7f13.dat nonoyes (1,7,19,13)(1,4,8,0) The same as nonextend.dat.
Sonoko Moriyama, Extendable shellability in dimension two, Bachelor's thesis.
Sonoko Moriyama and Fumihiko Takeuchi, Incremental construction properties in dimension two --- shellability, extendable shellability and vertex decomposability, preprint.