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 language | English |
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Pages (from-to) | 375-391 |
Number of pages | 17 |
Journal | Journal of the London Mathematical Society |
Volume | 50 |
Issue number | 2 |
DOIs | |
State | Published - Oct 1994 |
Externally published | Yes |