On a conjecture of A. J. Hoffman
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- by Joseph Zaks PDF
- Proc. Amer. Math. Soc. 27 (1971), 122-125 Request permission
Abstract:
A $3$-polytope $P$ and four closed convex sets ${C_1}, \cdots ,{C_4}$ in $P$ are described, having the following property: every line which meets $P$ meets at least one of the ${C_i}$’s, and for every collection of polytopes ${D_1}, \cdots ,{D_4}$, with ${D_i} \subseteq {C_i}$ for all $1 \leqq i \leqq 4$, there exists a line which meets $P$ and misses all of the ${D_i}$’s. This is a counterexample to a conjecture of A. J. Hoffman.References
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B. Grünbaum, Convex polytopes, Pure and Appl. Math., vol. 16, Interscience, New York, 1967. MR 37 #2085.
- A. J. Hoffman, On the covering of polyhedra by polyhedra, Proc. Amer. Math. Soc. 23 (1969), 123–126. MR 247570, DOI 10.1090/S0002-9939-1969-0247570-7
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 27 (1971), 122-125
- MSC: Primary 52.10
- DOI: https://doi.org/10.1090/S0002-9939-1971-0275282-1
- MathSciNet review: 0275282