Mathematische Zeitschrift

, Volume 188, Issue 4, pp 559–591

Regular and semi-regular polytopes. II

  • H. S. M. Coxeter
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1a.
    Coxeter, H.S.M.: Regular and semi-regular polytopes. I. Math. Z.46, 380–407 (1940)Google Scholar
  2. 1b.
    Berge, C.: Principles of combinatorics. New York: Academic Press 1971Google Scholar
  3. 2.
    Bourbaki, N.: Groupes et algèbres de Lie, Chapitres 4, 5 et 6. Paris: Hermann 1968Google Scholar
  4. 3.
    Brown, H., Bülow, R., Neubüser, J., Wondratschek, H., Zassenhaus, H.: Crystallographic groups of four-dimensional space. New York: Wiley 1978Google Scholar
  5. 4.
    Coxeter, H.S.M.: Groups whose fundamental regions are simplexes. J. London Math. Soc.6, 132–136 (1931)Google Scholar
  6. 5.
    Coxeter, H.S.M.: The polytopes with regular-prismatic vertex figures, I. Phil. Trans. Roy. Soc. London, A229, 329–425 (1930)Google Scholar
  7. 5a.
    Coxeter, H.S.M.: The polytopes with regular-prismatic vertex figures, II. Proc. London Math. Soc. (2)34, 126–189 (1932)Google Scholar
  8. 6.
    Coxeter, H.S.M.: Finite groups generated by reflections, and their subgroups generated by reflections. Proc. Cambridge Phil. Soc.30, 466–482 (1935)Google Scholar
  9. 7.
    Coxeter, H.S.M.: Extreme forms. Canad. J. Math.3, 391–441 (1951)Google Scholar
  10. 8.
    Coxeter, H.S.M.: Twelve geometric essays. Carbondale, IL.: Southern Illinois Univ. Press 1968Google Scholar
  11. 9.
    Coxeter, H.S.M.: Introduction to geometry (2nd. ed.). New York: Wiley 1969Google Scholar
  12. 10.
    Coxeter, H.S.M.: Twisted honeycombs. Regional Conference Series in Mathematics. Amer. Math. Soc.4 (1970)Google Scholar
  13. 11.
    Coxeter, H.S.M.: Regular polytopes (3rd. ed.). New York: Dover 1973Google Scholar
  14. 12.
    Coxeter, H.S.M.: Regular complex polytopes. Cambridge: Cambridge Univ. Press 1974Google Scholar
  15. 13.
    Coxeter, H.S.M.: Review of Merkel. Math. Rev.50, #14454, 1981–1982 (1975)Google Scholar
  16. 14.
    Coxeter, H.S.M.: Polytopes in the Netherlands. Nieuw Archief voor Wiskunde (3),26, 116–141 (1978)Google Scholar
  17. 15.
    Coxeter, H.S.M.: The edges and faces of a 4-dimensional polytope. Congressus Numerantium28, 309–334 (1980)Google Scholar
  18. 16.
    Coxeter, H.S.M., Huybers, P.: A new approach to the chiral Archimedean solids. C.R. Math. Rep. Acad. Sci. Canada1, 269–274 (1979)Google Scholar
  19. 17.
    Coxeter, H.S.M., Moser, W.O.J.: Generators and relations for discrete groups (4th ed.) Berlin Heidelberg New York: Springer 1980Google Scholar
  20. 18.
    Davis, C., Grünbaum, B., Sherk, F.A.: The geometric vein. Berlin Heidelberg New York: Springer 1980Google Scholar
  21. 19.
    Du Val P.: Homographies, quaternions and rotations. London: Oxford University Press 1964Google Scholar
  22. 20.
    Grünbaum, B.: Convex polytopes. New York: Interscience 1967Google Scholar
  23. 21.
    Hinton, C.H.: The fourth dimension. London: Swann Sonnenschein 1904Google Scholar
  24. 22.
    Hurley, A.C.: Finite rotation groups and crystal classes in four dimensions. Pages 571–586 of Quantum Theory of Atoms, Molecules, Solid State. New York: Academic Press 1966Google Scholar
  25. 23.
    Lines, L.: Solid geometry. London: Macmillan 1935Google Scholar
  26. 24.
    Merkel, J.: Sur le pavage de l'espace euclidien à 3 dimensions avec des cubes tronqués tordus, des icosaèdres et des tetraèdres. Ann. Univ. Mariae Curie-Skłodowska Sect. A,25, 41–65 (1971)Google Scholar
  27. 25.
    Salmon, G.: Analytic geometry of three dimensions, I (6th ed.). London: Longmans 1914Google Scholar
  28. 26.
    Schläfli, L.: Gesammelte Mathematische Abhandlungen, I. Basel: Birkhäuser 1950Google Scholar
  29. 27.
    Schoute, P.H.: Mehrdimensionale Geometrie, II. Leipzig: Göschen 1905Google Scholar
  30. 28.
    Sinkov, A.: The groups determined by the relations Sl=Tm=(S−1T−1ST)p=1. Duke Math. J.2, 74–83 (1936)Google Scholar
  31. 29.
    Tarnai, T.: Packing of 180 equal circles on a sphere. Elemente der Math.38, 119–122 (1983)Google Scholar
  32. 30.
    Warner, N.P.: The symmetry groups of the regular tessellations ofS 2 andS 3. Proc. Roy. Soc. London A383, 379–398 (1982)Google Scholar
  33. 31.
    Wythoff, W.A.: A relation between the polytopes of theC 600 family. K. Akad. Wetensch. te Amsterdam, Proc. Sect. Sci.20, 966–970 (1918)Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • H. S. M. Coxeter
    • 1
  1. 1.University of TorontoTorontoCanada

Personalised recommendations