Hostname: page-component-cc8bf7c57-7lvjp Total loading time: 0 Render date: 2024-12-11T22:17:40.434Z Has data issue: false hasContentIssue false
  • English
  • Français

The Number of Hexagons and the Simplicity of Geodesics on Certain Polyhedra

Published online by Cambridge University Press:  20 November 2018

B. Grünbaum  and
T. S. Motzkin
B. Grünbaum
Affiliation:
Hebrew University, Jerusalem and University of California, Los Angeles
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The problem of determining the possible morphological types of convex polyhedra in three-dimensional Euclidean space E3 is well known to be quite hopeless. We lack not only any general way of determining whether there exists a convex polyhedron having as faces ƒ3 triangles, ƒ4 quadrangles, . . . , and ƒnn-gons, but even much more special questions of this kind seem to be rather elusive.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 15 , 1963 , pp. 744 - 751
Copyright
Copyright © Canadian Mathematical Society 1963

References

1. Bruckner, M., Vielecke und Vielflache (Leipzig, 1900).Google Scholar
2. Eberhard, V., Zur Morphologie der Polyeder (Leipzig, 1891).Google Scholar
3. Griinbaum, B. and Motzkin, T. S., On polyhedral graphs, Proc. Symp. Pure Math., 7 (to appear).Google Scholar
4. Steinitz, E., Vorlesungen über die Théorie der Polyeder (Berlin, 1934).Google Scholar