Polytope projection and projection polytopes

American Mathematical Monthly

Volumn 103, Issue 9, 1996, Pages 742-755

  Burger, Thomas ^a   Gritzmann, Peter ^a   Klee, Victor ^b  

^a UNIVERSITY OF TRIER   (Germany)

^b UNIVERSITY OF WASHINGTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030519162     PISSN: 00029890     EISSN: None     Source Type: Journal    
DOI: 10.2307/2974444     Document Type: Article

References (27)

1. H. L. Bodlaender, P. Gritzmann, V. Klee, and J. van Leeuwen, Computational complexity of norm-maximization, Combinatorica 10 (1990), 203-225.
2. T. Bonnesen and W. Fenchel, Theorie der Konvexen Körper, Springer, Berlin, 1934, Reprint: Chelsea Publ. Co., New York, 1948, Translation: BCS Associates, Moscow, Idaho, 1987.
3. A. BrøSnsted, An Introduction to Convex Polytopes, Springer, New York, 1983.
4. R. C. Buck, Partition of space, Amer. Math. Monthly 50 (1943), 541-544.
5. T. Burger and P. Gritzmann, Finding optimal shadows of polytopes, in preparation, 1996.
6. H. G. Eggleston, Convexity, Cambridge Univ. Press, 1958.
7. M. R. Garey and D. S. Johnson, Computers and Intractability. A Guide to the Theory of NP-Completeness, Freeman, San Francisco, 1979.
8. P. Gritzmann and A. Hufnagel, A polynomial time algorithm for Minkowski reconstruction, Proc. 11th Ann. Symp. Comp. Geom., Association Comput. Mach., 1995, pp. 1-9.
9. P. Gritzmann and V. Klee, On the 0-1 maximization of positive definite quadratic forms, Operations Research Proceedings (D. Pressmar et al., eds.), Deutsche Gesellschaft für Operations Research, Springer, Berlin, 1989, pp. 222-227.
10. _, Inner and outer j-radii of convex bodies in finite-dimensional normed spaces, Discrete Comput. Geom. 7 (1992), 255-280.
11. _, Some basic problems in computational convexity: II. Volume and mixed volumes, In: Polytopes: Abstract, Convex and Computational (T. Bisztriczky, P. McMullen, R. Schneider, and A. Ivic Weiss, eds.), Kluwer, Boston, 1994, pp. 373-466.
12. B. Grünbaum, Convex Polytopes, Wiley-Interscience, London, 1967.
13. H. Martini, Some characterizing properties of the simplex, Geom. Dedicata 29 (1989), 1-6.
14. _, A new view on some characterizations of simplices, Arch. Math. 55 (1990), 389-393.
15. _, Cross-sectional measures, Coll. Math. Soc. J. Bolyai, North-Holland, Amsterdam, 1994, pp. 269-310.
16. H. Martini and B. Weissbach, Zur besten Beleuchtung konvexer Polyeder, Beitr., Algebra Geom. 17 (1984), 151-168.
17. _, On quermasses of simplices, Studia Sci. Math. Hung. 27 (1992), 213-222.
18. M. McKenna and R. Seidel, Finding the optimal shadow of a convex polytope, Proc. 1st Symp. Comp. Geom., Association Comput. Mach., 1985, pp. 24-28.
19. P. McMullen, The maximum number of faces of a convex polytope, Mathematika 17 (1970), 179-184.
20. P. McMullen and G. C. Shephard, Convex Polytopes and the Upper Bound Conjecture, Cambridge Univ. Press, 1971.
21. H. Minkowski, Allgemeine Lehrsätze über die konvexen Polyeder, Nachr. Ges. Wiss. Göttingen (1897), 198-219.
22. _, Volumen und Oberfläche, Math. Ann. 57 (1903), 447-495.
23. C. A. Rogers and G. C. Shephard, The difference body of a convex body, Arch. Math. 8 (1957), 220-233.
24. R. Schneider, Convex Bodies: The Brunn-Minkowski Theory, Encyclopedia of Mathematics and its Applications, vol. 44, Cambridge Univ. Press, 1993.
25. A. Schrijver, Theory of Linear and Integer Programming, Wiley-Interscience, New York, 1986.
26. T. Zaslavsky, Facing up to Arrangements: Face-Count Formulas for Partitions of Space by Hyperplanes, American Mathematical Society Memoirs, vol. 154, Amer. Math. Soc., 1975.
27. G. M. Ziegler, Lectures on Polytopes, Graduate Texts in Mathematics, vol. 152, Springer-Verlag, New York-Berlin-Heidelberg, 1995.