Regular and semi-regular polytopes. III (original) (raw)
References
Coxeter, H.S.M.: Regular and semi-regular polytopes. I. Math. Z.46, 380–407 (1940) Google Scholar
Coxeter, H.S.M.: Regular and semi-regular polytopes. II. Math. Z.188, 559–591 (1985) Google Scholar
Atkinson, M.D.: How to compute the series expansions of sec_x_ and tan_x_. Am. Math. Monthly93, 387–388 (1986) Google Scholar
Ball, W.W.R., Coxeter, H.S.M.: Mathematical Recreations and Essays (13th ed.). New York: Dover 1987 Google Scholar
Barth, W., Knörrer, H.: Algebraische Flächen, Chapter 2 in Mathematische Modelle, Kommentarband, ed. Gerd Fischer. Braunschweig-Wiesbaden: Vieweg 1986 Google Scholar
Blij, F. van der: History of the octaves. Simon Stevin3, 106–125 (1961) Google Scholar
Blij, F. van der: Units of octaves. Indagationes Math.28, 127–130 (1966) Google Scholar
Bourbaki, N.: Groupes et algèbres de Lie, Chapitres 4, 5, et 6. Paris: Hermann 1968 Google Scholar
Bromwich, T.J.I'a: An Introduction to the Theory of Infinite Series. London: Macmillan 1908 Google Scholar
Cayley, A.: Collected mathematical papers I. Cambridge: Cambridge Univ. Press 1889 Google Scholar
Conway, J.H., Curtis, R.T., Norton, S.P., Parker, R.A., Wilson, R.A.: Atlas of finite groups. Oxford: Clarendon 1985 Google Scholar
Conway, J.H., Parker, R.A., Sloane, N.J.A.: The covering radius of the Leech latice. Proc. r. Soc. London, A380, 261–290 (1982) Google Scholar
Conway, J.H., Sloane, N.J.A.: Sphere packings, lattices and groups. Berlin, Heidelberg, New York: Springer 1988 Google Scholar
Coxeter, H.S.M.: The pure Archimedean polytopes in six and seven dimensions. Proc. Camb. Philos. Soc.24, 1–9 (1928) Google Scholar
Coxeter, H.S.M.: The polytopes with regular-prismatic vertex figures. I. Phil. Trans. Roy. Soc. London, A229, 329–425 (1930) Google Scholar
Coxeter, H.S.M.: Groups whose fundamental regions are simplexes. J. London Math. Soc.6, 132–136 (1931) Google Scholar
Coxeter, H.S.M.: The polytopes with regular-prismatic vertex figures. II. Proc. London Math. Soc. (2)34, 126–189 (1932) Google Scholar
Coxeter, H.S.M.: Discrete groups generated by reflections. Annals of Math.35, 588–621 (1934) Google Scholar
Coxeter, H.S.M.: The polytope 221, whose 27 vertices correspond to the lines on the general cubic surface. Am. J. Math.62, 457–486 (1940) Google Scholar
Coxeter, H.S.M.: Extreme forms. Can. J. Math.3, 339–441 (1951) Google Scholar
Coxeter, H.S.M.: The product of the generators of a finite group generated by reflections. Duke Math. J.18, 765–782 (1951) Google Scholar
Coxeter, H.S.M.: Non-Euclidean geometry (5th ed.). Toronto: Toronto University Press 1965 Google Scholar
Coxeter, H.S.M.: Polytopes in the Netherlands. Nieuw Archief voor Wiskunde (3)26, 116–141 (1978) Google Scholar
Coxeter, H.S.M., Edge, W.L.: The simple groups PSL(2, 7) and PSL(2, 11). C.R. Math. Rep. Acad. Sci. Canada5, 201–206 (1983) Google Scholar
Coxeter H.S.M., Longuet-Higgins, M.S., Miller, J.C.P.: Uniform polyhedra. Phil. Trans. Roy. Soc. London A246, 401–450 (1954) Google Scholar
Davis, C., Grünbaum, B., Sherk, F.A.: The geometric vein. Berlin, Heidelberg, New York: Springer 1980 Google Scholar
Dickson, L.E.: On quaternions and their generalization and the history of the eight square theorem. Ann. Math. (2)20, 115–171 (1919) Google Scholar
Du Val, P.: On the Kantor group of a set of points in a plane. Proc. London Math. Soc. (2)42, 18–51 (1937) Google Scholar
Dynkin, E.B.: Classification of simple Lie groups. Rec. Math. (Mat. Sbornik) N.S.18, (60), 347–352 (1946) Google Scholar
Dynkin, E.B., Oniščik, A.L.: Compact local Lie groups. Uspechi Mat. Nauk (N.S.)10, no. 4 (66), 3–74 (1955) Google Scholar
Frame, J.S.: A symmetric representation of the twenty-seven lines on a cubic surface by lines in a finite geometry. Bull. Am. Math. Soc.44, 658–661 (1938) Google Scholar
Frame, J.S.: Characteristic vectors for a product of_n_ reflections. Duke Math. J.18, 783–785 (1951) Google Scholar
Gosset, T.: On the regular and semi-regular figures in space of_n_ dimensions. Messenger of Math.29, 43–48 (1900) Google Scholar
Grove, L.C., Benson, C.T.: Finite reflection groups (2nd. ed.). New York: Springer 1985 Google Scholar
Gruber, P., Wills, J.M.: Convexity and its applications. Basel: Birkhäuser Verlag 1983 Google Scholar
Hargittai, I.: Symmetry unifying human understanding, II. New York: Pergamon Press 1988 Google Scholar
Hilbert, D., Cohn-Vossen, S.: Anschauliche Geometrie. Berlin Heidelberg New York: Springer 1973. Translated as Geometry and the imagination. New York: Chelsea 1952 Google Scholar
Hirschfeld, J.W.P.: A configuration of lines in three dimensions. Proc. Edinb. Math. Soc. (2)18, 105–123 (1972/73) Google Scholar
Leech, J.: Six and seven dimensional non-lattice sphere packings. Can. Math. Bull.12, 151–155 (1969) Google Scholar
Lemmens, P.W.H., Seidel, J.J.: Equiangular lines. J. Algebra24, 494–512 (1973) Google Scholar
Lint, J.H. van, Seidel, J.J.: Equilateral point sets in elliptic geometry. Indagationes Math.28, 335–348 (1966) Google Scholar
Longuet-Higgins, M.S.: Clifford's chain and its analogues in relation to the higher polytopes. Proc. Roy. Soc. London A330, 443–466 (1972) Google Scholar
Macrobert, T.M.: Functions of a complex variable (2nd. ed.). London: Macmillan 1933 Google Scholar
Melzak, Z.A.: Companion to concrete mathematics. New York: Wiley 1973 Google Scholar
Miller, G.A., Blichfeldt, H.F., Dickson, L.E.: Theory and applications of finite groups (1st. ed.). New York: Wiley 1916 Google Scholar
Monson, B.R.: A family of uniform polytopes with symmetric shadows. Geom. Dedicata23, 355–363 (1987) Google Scholar
Neumaier, A.: Lattices of simplex type. SIAM J. Algebraic Discrete Methods4, 145–160 (1983) Google Scholar
Rankine, W.J.M.: Principle of the equilibrium of polyhedral frames. Phil. Mag. (4)27, 92 (1862) Google Scholar
Schläfli, L.: Gesammelte Mathematische Abhandlungen, I. Basel: Verlag Birkhäuser 1950 Google Scholar
Schläfli, L.: Gesammelte Mathematische Abhandlungen, II. Basel: Verlag Birkhäuser 1953 Google Scholar
Schoute, P.H.: On the relation between the vertices of a definite six-dimensional polytope and the lines of a cubic surface. K. Akad. Wetenschappen te Amsterdam, Proceedings of the Section of Sciences,13, 375–383 (1910) Google Scholar
Shephard, G.C., Todd, J.A.: Finite unitary reflection groups. Can. J. Math.6, 274–304 (1954) Google Scholar
Solomon, L.: Invariants of finite reflection groups. Nagoya Math. J.22, 57–64 (1963) Google Scholar
Tits, J.: Géométries polyédriques finies. Rendiconti di Mat.23, 156–165 (1964) Google Scholar
Todd, J.A.: Polytopes associated with the general cubic surface. J. London Math. Soc.7, 200–205 (1932) Google Scholar
Weiss, A.I.: A four-dimensional projection of the polytope 221 C.R. Math. Rep. Acad. Sci. Canada8, 405–410 (1986) Google Scholar
Witt, E.: Spiegelungsgruppen und Aufzählung halbeinfacher Liescher Ringe. Abh. Math. Semin. Hansischen Univ.14, 289–322 (1941) Google Scholar