Bing's house with two rooms

Description

A famous example of a triangulation of a 3-ball, made by Bing. The two-dimensional version of this example (the left figure) is a very famous 2-polyhedron which is non-collapsible but contractible. The object in the left figure is made by two-dimensional panels, with two rooms. The upper room is to be entered from the bottom face, and the lower room is to be entered from the upper face. (The two small pannels attached to the tunnels make this object to be contractible.)

If we replace every two-dim pannels by a one-layered pile of cubes and triangulate each cube into six tetrahedra (as in the right figure) we get a triangulated 3-ball and it is not shellable.

The data given here has 480 vertices and 1554 facets.

Properties

This is known as a non-shellable triangulation of a 3-ball, but in fact this is not constructible, either.

Datum

bing.dat

Table

vertex decomposable?	no
extendably shellable?	no
shellable?	no
constructible?	no
Cohen-Macaulay?	yes
topology	3-ball
f-vector	(1,480,2511,3586,1554)
h-vector	(1,476,1077,0,0)
made by	Bing

References

R.H.Bing, Some aspects of the topology of 3-manifolds related to the Poincar\'e Conjecture, Lectures on Modern Mathematics II, T.L. Saaty ed., Wiley (1964), 93-128.

M.Hachimori, Nonconstructible simplicial balls and a way of testing constructibility, Discrete Comput. Geom. 22 (1999), 223-230.

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