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Collapsing three-dimensional convex polyhedra

Published online by Cambridge University Press:  24 October 2008

D. R. J. Chillingworth
D. R. J. Chillingworth
Affiliation:
St John's College, Cambridge
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Extract

If L is a subcomplex of a simplicial complex K, we say that L is obtained from K by an elementary simplical collapse if K − L consists of a simplex σ of some dimension d together with one ‘free’ face of σ, i.e. a face τ of dimension d − 1 which is a face of no other simplex of K except σ. Such a collapse is said to take place through σ from τ. If L can be obtained from K by a finite sequence of elementary simplicial collapses we say that K simplicially collapses (s-collapses) onto L, denoted by K ↘ L

If K is regarded as being embedded in some Euclidean space we shall for convenience of notation fail to distinguish between K and its underlying polyhedron.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 2 , April 1967 , pp. 353 - 357
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

(1)Bing, R. H. Some aspects of the topology of 3-manifolds related to the Poincaré conjecture. Lectures on modern mathematics, vol. II. Ed. Saaty., T. L.John Wiley and Sons, Inc. (1964).Google Scholar
(2)Rudin, M. E.An unshellable triangulation of a tetrahedron. Bull. Amer. Math. Soc. 64 (1958), 90–91.CrossRefGoogle Scholar