Mani & Walkup's 3-sphere(D)

Description

Mani and Walkup's 3-sphere which is not vertex decomposable. This example is made from their another sphere (mani-walkup-C.dat) to reduce the number of faces a little. Called "D" in the paper.

Properties

In the paper, it is written that whether this 3-sphere is shellable or not known to the authors. But my recent calculation on the computer showed that this sphere is shellable. Here is a shelling.

Datum

mani-walkup-D.dat

Some table

vertex decomposable?	no
extendably shellable?	?
shellable?	open problem yes
constructible?	?
Cohen-Macaulay?	yes
partitionable?	yes
topology	3-sphere
f-vector	(1,16,106,180,90)
h-vector	(1,12,64,12,1)
made by	Mani&Walkup

References

P.Mani and D.W.Walkup, A 3-sphere counterexample to the $W_v$-path conjecture, Math. Operations Research 5 (1980), 595-598.