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No nine neighborly tetrahedra exist


About this Title

Joseph Zaks

Publication: Memoirs of the American Mathematical Society
Publication Year 1991: Volume 91, Number 447
ISBNs: 978-0-8218-2517-4 (print); 978-1-4704-0873-2 (online)
DOI: http://dx.doi.org/10.1090/memo/0447
MathSciNet review: 1070040
MSC: Primary 52B11; Secondary 51M20

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Table of Contents


Chapters

  • 1. The Baston matrix; the 24 solutions
  • 2. Cases #4, 5, 7, 8, 11, 14, 15, 19 and #24
  • 3. Types of tetrahedra
  • 4. The use of the Baston matrices
  • 5. Computer search for case #2
  • 6. Computer search for case #3
  • 7. Computer search for case #6, 9 and #10
  • 8. Computer search for case #12, 16, 17 and #18
  • 9. Computer search for case #20, 21, 22 and #23; end of the proof
  • 10. On eight neighborly tetrahedra
  • 11. At most fourteen nearly-neighborly tetrahedra
American Mathematical Society