Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 61: Issue 1
A Combinatorial Construction of Bi-Cyclic 4-Polytopes
Author:
Tibor Bisztriczky University of Calgary, Calgary, Alberta, T2N 1N4, Canada

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Pages:
73–87
Online Publication Date:
15 Apr 2024
Publication Date:
15 Apr 2024
Article Category:
Research Article
DOI:
https://doi.org/10.1556/012.2024.04305
Keywords:
4-polytope; vertex array; Gale condition; geometric lattice
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A bi-cyclic 4-polytope in ℝ4 was introduced by Z. Smilansky as the convex hull of evenly spaced points on a generalized trigonometric moment curve in ℝ4. We present combinatorial geometric conditions that yield the face lattices of a class of such 4-polytopes.

  • [1]

    T. Bisztriczky and K. Böröczky, Jr. On periodically-cyclic Gale 4-polytopes. Disc. Math., 241:103–118, 2001.

  • [2]

    D. Gale. Neighborly and cyclic polytopes. Proc. Sympos. Pure Math., 7 (Convexity):225–232, 1963.

  • [3]

    B. Grünbaum. Convex Polytopes. Springer, GTM 221, 2003.

  • [4]

    Z. Smilansky. Convex hulls of generalized moment curves. Isr. J. Math., 52:115–128, 1985.

  • [5]

    Z. Smilansky. Bi-cyclic 4-polytopes. Isr. J. Math., 70:82–92, 1990.

  • [6]

    G. M. Ziegler. Lectures on polytopes. Springer, GTM 152, 1995.

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Cover Studia Scientiarum Mathematicarum Hungarica
Studia Scientiarum Mathematicarum Hungarica
Print ISSN:
0081-6906
Online ISSN:
1588-2896

Editors in Chief

Gábor SIMONYI (Rényi Institute of Mathematics)
András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics) 

Managing Editor

Gábor SÁGI (Rényi Institute of Mathematics)

Editorial Board

  • Imre BÁRÁNY (Rényi Institute of Mathematics)
  • Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
  • Péter CSIKVÁRI (ELTE, Budapest) 
  • Joshua GREENE (Boston College)
  • Penny HAXELL (University of Waterloo)
  • Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
  • Ron HOLZMAN (Technion, Haifa)
  • Satoru IWATA (University of Tokyo)
  • Tibor JORDÁN (ELTE, Budapest)
  • Roy MESHULAM (Technion, Haifa)
  • Frédéric MEUNIER (École des Ponts ParisTech)
  • Márton NASZÓDI (ELTE, Budapest)
  • Eran NEVO (Hebrew University of Jerusalem)
  • János PACH (Rényi Institute of Mathematics)
  • Péter Pál PACH (BME, Budapest)
  • Andrew SUK (University of California, San Diego)
  • Zoltán SZABÓ (Princeton University)
  • Martin TANCER (Charles University, Prague)
  • Gábor TARDOS (Rényi Institute of Mathematics)
  • Paul WOLLAN (University of Rome "La Sapienza")

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Studia Scientiarum Mathematicarum Hungarica
Language English
French
German
Size B5
Year of
Foundation		 1966
Volumes
per Year		 1
Issues
per Year		 4
Founder Magyar Tudományos Akadémia  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0081-6906 (Print)
ISSN 1588-2896 (Online)

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