Abstract
A convex d-polytope in ℝd is called edge-antipodal if any two vertices that determine an edge of the polytope lie on distinct parallel supporting hyperplanes of the polytope. We introduce a program for investigating such polytopes, and examine those that are simple.
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References
K. Bezdek, T. Bisztriczky and K. Böröczky, Edge-antipodal 3-polytopes, Disc. and Comp. Geometry (J. E. Goodman, J. Pach and E. Webzl, eds.), MSRI, Cambridge University Press, 2005, 129–134.
T. Bisztriczky and K. Böröczky, On antipodal 3-polytopes, Rev. Roumaine Math. Pures Appl., 50 (2005), 477–481.
B. Csikós, Edge-antipodal convex polytopes — a proof of Talata’s conjecture, Discrete Geometry (A. Bezdek, ed.) Pure Appl. Math. 253, Dekker, New York, 2003, 201–205.
L. Danzer and B. Grünbaum, Über zwei Probleme bezüglich konvexer Körper von P. Erdős und von V. Klee, Math. Z., 79 (1962), 95–99.
B. Grünbaum, Convex Polytopes, Springer, New York, 2003.
P. McMullen, Polytopes with parathetic faces, Rev. Roumaine Math. Pures Appl., 51 (2005), 65–76.
C. M. Petty, Equilateral sets in Minkowski spaces, Proc. Amer. Math. Soc., 29 (1971), 369–374.
A. Pór, On e-antipodal polytopes, submitted.
A. Schürmann and K. Swanepoel, Three-dimensional antipodal and normequilateral sets, Pacific J. Math., 228 (2006), 349–370.
K. Swanepoel, Upper bounds for edge-antipodal and subequilateral polytopes, Period. Math. Hungar., 54 (2007), 99–106.
I. Talata, On extensive subsets of convex bodies, Period. Math. Hungar., 38 (1999), 231–246.
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Bisztriczky, T., Böröczky, K. On edge-antipodal d-polytopes. Period Math Hung 57, 131–141 (2008). https://doi.org/10.1007/s10998-008-8131-5
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DOI: https://doi.org/10.1007/s10998-008-8131-5