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McMullen, P.

On zonotopes. (English) Zbl 0223.52007

Trans. Am. Math. Soc. 159, 91-109 (1971).
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52B35 Gale and other diagrams
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\textit{P. McMullen}, Trans. Am. Math. Soc. 159, 91--109 (1971; Zbl 0223.52007)
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References:

[1] E. Bonnice and L. M. Kelly, On the number of ordinary planes, J. Combinatorial Theory (to appear). · Zbl 0225.52006
[2] H. S. M. Coxeter, The classification of zonohedra by means of projective diagrams, J. Math. Pures Appl. (9) 41 (1962), 137 – 156. · Zbl 0123.13701
[3] G. A. Dirac, Collinearity properties of sets of points, Quart. J. Math., Oxford Ser. (2) 2 (1951), 221 – 227. · Zbl 0043.14602 · doi:10.1093/qmath/2.1.221
[4] P. Erdos, Richard Bellman, H. S. Wall, James Singer, and V. Thébault, Problems and Solutions: Advanced Problems: Problems for Solution: 4065-4069, Amer. Math. Monthly 50 (1943), no. 1, 65 – 66. · doi:10.2307/2304011
[5] David Gale, Neighboring vertices on a convex polyhedron, Linear inequalities and related system, Annals of Mathematics Studies, no. 38, Princeton University Press, Princeton, N.J., 1956, pp. 255 – 263. · Zbl 0072.37805
[6] Grünbaum, Convex polytopes, Pure and Appl. Math., vol. 16, Interscience, New York, 1967. MR 37 #2085. · Zbl 0152.20602
[7] Sten Hansen, A generalization of a theorem of Sylvester on the lines determined by a finite point set, Math. Scand. 16 (1965), 175 – 180. · Zbl 0156.19501 · doi:10.7146/math.scand.a-10758
[8] L. M. Kelly and W. O. J. Moser, On the number of ordinary lines determined by \? points, Canad. J. Math. 10 (1958), 210 – 219. · Zbl 0081.15103 · doi:10.4153/CJM-1958-024-6
[9] P. McMullen, Linearly stable polytopes, Canad. J. Math. 21 (1969), 1427 – 1431. · Zbl 0187.19602 · doi:10.4153/CJM-1969-157-4
[10] P. McMullen and G. C. Shephard, Diagrams for centrally symmetric polytopes, Mathematika 15 (1968), 123 – 138. · Zbl 0167.50902 · doi:10.1112/S0025579300002473
[11] -, Convex polytopes and the upper-bound conjecture, London Math. Soc. Lecture Note Series, vol. 3, 1971. · Zbl 0217.46702
[12] Th. Motzkin, The lines and planes connecting the points of a finite set, Trans. Amer. Math. Soc. 70 (1951), 451 – 464. · Zbl 0043.14603
[13] Pólya, Kombinatorische Anzahlbestimmungen für Gruppen, Graphen und chemische Verbindungen, Acta Math. 68 (1937), 145-254, 217, 232. · JFM 63.0547.04
[14] G. C. Shephard, Diagrams for positive bases, J. London Math. Soc. (2) 4 (1971), 165 – 175. · Zbl 0225.15004 · doi:10.1112/jlms/s2-4.1.165
[15] Steinitz, Bedingt konvergente Reihen und konvexe Systeme. II, J. Reine Angew. Math. 144 (1914), 1-40. FM 44, 287. · JFM 45.0380.01
[16] J. Sylvester, Mathematical question 11851, Ed. Times 59 (1893), 98.
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