Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-24T11:45:34.505Z Has data issue: false hasContentIssue false
  • English
  • Français

The number of simplicial neighbourly d-polytopes with d+3 vertices

Published online by Cambridge University Press:  26 February 2010

A. Altshuler  and
P. McMullen
A. Altshuler
Affiliation:
University of the Negev, Beer-Sheva, Israel.
P. McMullen
Affiliation:
University College London.
Get access

Abstract

In this paper is proved a formula for the number of simplicial neighbourly d-polytopes with d + 3 vertices, when d is odd.

Type
Research Article
Information
Mathematika , Volume 20 , Issue 2 , December 1973 , pp. 263 - 266
Copyright
Copyright © University College London 1973

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Altshuler, A., “Polyhedral realization in R3 of triangulations of the torus and 2-manifolds in cyclic 4-polytopes”, Discrete Maths., 1 (1971), 211–238.CrossRefGoogle Scholar
Altshuler, A., “Vertex figures of cyclic polytopes”, Notices Amer Math Soc. 19 (1972), A192.Google Scholar
Altshuler, A. and Steinberg, L., “Neighborly 4-polytopes with 9 vertices”, J. Combinatorial Theory, Ser A, 15 (1973), 270–287.CrossRefGoogle Scholar
Grünbaum, B., Convex polytopes (Wiley and Sons, London, New York, Sydney, 1967).Google Scholar
Grünbaum, B. and Sreedharan, V. P., “An enumeration of simplicial 4-polytopes with 8 vertices”, J. Combinatorial Theory, 2 (1967), 437–465.CrossRefGoogle Scholar
McMullen, P., “The maximum numbers of faces of a convex polytope”, Mathematika, 17 (1970), 179–184.CrossRefGoogle Scholar
McMullen, P. and Shephard, G. C., Convex polytopes and the upper-bound conjecture, London Math. Soc. Lecture Notes Series, Vol. 3 (Cambridge University Press, 1971).Google Scholar
Motzkin, T. S., “Comonotone curves and polyhedra”, Abstract 111, Bull. Amer. Math. Soc., 63 (1957), 35.Google Scholar
Póya, G., “Combinatorische Anzahlbestimmungen für Gruppen, Graphen und chemische Verbindungen”, Acta Math., 68 (1937), 145–254.Google Scholar
Shephard, G. C., “A theorem on cyclic polytopes”, Israel J. Math., 6 (1968), 368–372.CrossRefGoogle Scholar