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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
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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

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4. Steinitz, E., Vorlesungen über die Théorie der Polyeder (Berlin, 1934).Google Scholar