Successive Determination and Verification of Polytopes by their X-Rays

R. J. Gardner, Peter Gritzmann

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

It is shown that each convex polytope P in 피dcan be verified by ([d/(d–k)] + 1) k-dimensional X-rays. This means that P is uniquely determined by these X-rays and the choice of the direction of each X-ray depends only on P. Examples are constructed to show that in general this number cannot be reduced. Further, it is shown that each convex polytope P in 피3can be successively determined by only two one-dimensional X-rays. This means that P is uniquely determined by one X-ray taken in an arbitrary direction together with another whose direction depends only on the first X-ray. The results extend those for the case d = 2 of Giering and of Edelsbrunner and Skiena.

Original languageEnglish
Pages (from-to)375-391
Number of pages17
JournalJournal of the London Mathematical Society
Volume50
Issue number2
DOIs
StatePublished - Oct 1994
Externally publishedYes

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