Abstract
The notions of local similarity and decomposability are extended to the class of geometric graphs. These, in turn, are used to produce new sufficient conditions for indecomposability of polytopes. A simple example is given of two combinatorially equivalent 3-polytopes, one decomposable, and the other not.
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References
D. Gale,Irreducible convex sets, Proc. International Congress of Math., Amsterdam, 1954, II, p. 217.
B. Grünbaum,Convex Polytopes, John Wiley and Sons, London, 1967.
M. Kallay,Decomposability of convex polytopes, Ph.D. thesis, The Hebrew University of Jerusalem, 1979.
W. Meyer,Minkowski addition of convex sets, Ph.D. dissertation, University of Wisconson, Madison, 1969.
W. Meyer,Indecomposable polytopes, Trans. Amer. Math. Soc.190 (1974), 77–86.
D. Pedoe,An Introduction to Projective Geometry, Pergamon Press, Oxford, 1963.
G. C. Shephard,Decomposable convex polyhedra, Mathematika10 (1963), 89–95.
G. C. Shephard,Spherical complexes and radial projections of polytopes, Israel J. Math.9 (1971), 257–262.
R. Silverman,Decomposition of plane convex sets, Part 1, Pacific J. Math.47 (1973), 521–530.
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The content of this paper is an extension of a part of a Ph.D. thesis [3], written by the author under the supervision of Professor M. A. Perles at the Hebrew University of Jerusalem, and submitted in April 1979.
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Kallay, M. Indecomposable polytopes. Israel J. Math. 41, 235–243 (1982). https://doi.org/10.1007/BF02771723
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DOI: https://doi.org/10.1007/BF02771723