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.
Similar content being viewed by others
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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10998-008-8131-5