On a conjecture of a.J.Hoffman

Research output: Contribution to journalArticlepeer-review


A 3-polytope P and four closed convex sets C1,;…, C4 in P are described, having the following property: every line which meets P meets at least one of the Ci ‘ s, and for every collection of polytopes D1, …, D4, with Di⊆ Ci for all 1≦ i≦ 4, there exists a line which meets P and misses all of the Di‘ s. This is a counterexample to a conjecture of A. J. Hoffman.

Original languageEnglish
Pages (from-to)122-125
Number of pages4
JournalProceedings of the American Mathematical Society
Issue number1
StatePublished - Jan 1971
Externally publishedYes


  • Affine t-flat
  • Closed convex set
  • Convex d-polytype
  • Convex planar curve

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics


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