Rudin's 3ball
 Description

Rudin showed in her 1958 paper that we can triangulate a 3tetrahedron
by introducing 10 vertices on the boundary in such a way that the
resulting triangulation is not shellable.
This triangulation has 14 vertices and 41 facets.
An interesting fact is that all the vertices can be perturbed into
a position that the 3ball is strictly convex, that is, this achieve
a nonshellable 3ball with a convex realization.
 Properties

Chillingworth(1967)'s theorem shows this triangulation is
simplicially collapsible.
Also this example is known to be constructible.
 Datum

rudin.dat
 Some table

vertex decomposable?  no 
extendably shellable?  no 
shellable?  no 
constructible?  yes 
CohenMacaulay?  yes 
partitionable?  yes 
topology  3ball 
fvector  (1,14,66,94,41) 
hvector  (1,10,30,0,0) 
made by  Rudin 
 References
 M.E.Rudin,
An unshellable triangulation of a tetrahedron,
Bulltin Amer. Math. Soc. 64 (1958), 9091.
 D.R.J. Chillingworth,
Collapsing threedimensional convex polyhedra,
Math. Proc. Camb. Phil. Soc. 63 (1967), 353357.
(Errata in Math. Proc. Camb. Phil. Soc. 88 (1980), 307310.)
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