Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-24T12:45:31.441Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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