The Mathematical Intelligencer

, Volume 5, Issue 3, pp 11–22 | Cite as

The 9-vertex complex projective plane

  • Wolfgang Kühnel
  • Thomas F. Banchoff


Projective Plane Euler Characteristic Equilateral Triangle Height Function Real Projective Plane 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    E. Bertini (1907) Geometria proiettiva degli iperspazi, Pisa, (Gennari translation (1924) Einführung in die projektive Geometrie mehrdimensionaler Räume, Wien)Google Scholar
  2. 2.
    H. S. M. Coxeter (1974) The Equianharmonic Surface and the Hessian Polyhedron,Annali di Mat. 98:77–92CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    H. S. M. Coxeter and W. O. J. Moser (1980) Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag (Ergebnisse der Mathematik und ihrer Grenzgebiete 14)Google Scholar
  4. 4.
    B. Grünbaum and V. P. Sreedharan (1967) An Enumeration of Simplicial 4-Polytopes with 8 Vertices,J. Comb. Theory 2:437–465CrossRefMATHGoogle Scholar
  5. 5.
    W. Kühnel and G. Laβmann (to appear) The unique 3- neighborly 4-manifold with few vertices,J. Comb. Th. (A)Google Scholar
  6. 6.
    N. H. Kuiper (1962) On convex maps,Nieuw Archief voor Wisk. 10:147–164MATHMathSciNetGoogle Scholar
  7. 7.
    N. H. Kuiper (1974) The quotient space of CP(2) by complex conjugation is the 4-sphere, Math. Ann. 208:175–177Google Scholar
  8. 8.
    N. H. Kuiper (1980) Tight Embeddings and Maps. Submanifolds of Geometrical Class Three in EN, Proc. Chern. Symp. Berkeley 1979, Springer-Verlag, pp. 97–145Google Scholar
  9. 9.
    N. H. Kuiper and W. F. Pohl (1977) Tight topological embeddings of the real projective plane in E5,Invent. Math. 42:177–199CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    G. Mannoury (1900) Surfaces-images,Nieuw Archief voor Wiskunde 4:112–129.MATHGoogle Scholar
  11. 11.
    W. S. Massey (1973) The quotient space of the complex projective plane under conjugation is a 4-sphere,Geo- metriae Dedicata 2:371–374MATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 1983

Authors and Affiliations

  • Wolfgang Kühnel
    • 1
  • Thomas F. Banchoff
    • 2
  1. 1.Fachbereich Mathematik Technische UniversitätBerlin (West) 12Germany
  2. 2.Mathematics DepartmentBrown UniversityProvidenceUSA

Personalised recommendations