A peculiar triangulation of the 3-sphere

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A triangulation of the 3-sphere with 10 vertices is presented, which is not directly obtainable by a generalized stellar subdivision from any 3-sphere with 9 vertices. This answers in the affirmative a conjecture by B. Griinbaum. This example is shown to be the minimal possible.

Original languageEnglish
Pages (from-to)449-452
Number of pages4
JournalProceedings of the American Mathematical Society
Issue number1
StatePublished - 1 Jan 1976


  • Combinatorial n-sphere
  • Shellable sphere
  • Simplicial n-complex


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