A 3sphere with a knotted triangle

Lickorish (1991) showed the there are nonshellable
triangulations of a 3sphere.
What he showed is the fact that if a triangulation of a 3sphere
contain a knot made of 3 edges in the 1skeleton, then it is
not shellable.
What he suggested to make such a triangulation is to use the
following construction.
First, we prepare the Furch's 3ball
with a knotted spanning arc consisting of one edge.
Then we take a cone over the boundary of the ball, then we have
a triangulated 3sphere with a knot made of 3 edges.
The data given here is made from knot.dat
by onepoint compactification. This has 381vertices and 1928 facets.
 Properties

Lickorish's original theorem asserts that the triangulation is
nonshellable if the knot embedded is "complex enough",
but in fact, it is not shellable (even not constructible)
if the knot is nontrivial.
 Datum

nc_sphere.dat
 Table

vertex decomposable?  no 
extendably shellable?  no 
shellable?  no 
constructible?  no 
CohenMacaulay?  yes 
topology  3sphere 
fvector  (1,381,2309,3856,1928) 
hvector  (1,377,1172,377,1) 
made by  Lickorish (またはfolklore) 
 References
 W.B.R.Lickorish,
Unshellable triangulations of spheres,
Europ. J. Cominatorics 12 (1991), 527530.
 M.Hachimori and G.M.Ziegler,
Decompositions of balls and spheres with knots consisting of few edges,
Math. Z., to appear.
Remark:
A sophisticated triangulation using this knot idea is provided by F. Lutz in:

F.H. Lutz, Small examples of nonconstructible simplicial balls and spheres,
SIAM J. Discrete Math. 18, 103109 (2004).
It uses only 13 vertices and 56 facets!
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