Indecomposable polytopes
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- by Walter Meyer PDF
- Trans. Amer. Math. Soc. 190 (1974), 77-86 Request permission
Abstract:
The space of summands (with respect to vector addition) of a convex polytope in n dimensions is studied. This space is shown to be isomorphic to a convex pointed cone in Euclidean space. The extreme rays of this cone correspond to similarity classes of indecomposable polytopes. The decomposition of a polytope is described and a bound is given for the number of indecomposable summands needed. A means of determining indecomposability from the equations of the bounding hyperplanes is given.References
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J. D. Flowers, Facial cones, local similarity and indecomposability of polytopes, Ph D. Thesis, Oklahoma State University, Stillwater, Okla., 1966.
D. Gale, Irreducible convex sets, Proc. I.C.M. Amsterdam, 1954, II, 217-218.
- Branko Grünbaum, Measures of symmetry for convex sets, Proc. Sympos. Pure Math., Vol. VII, Amer. Math. Soc., Providence, R.I., 1963, pp. 233–270. MR 0156259 —, Convex polytopes, Pure and Appl. Math., vol. 16, Interscience, New York, 1967. MR 37 #2085.
- P. McMullen, Representations of polytopes and polyhedral sets, Geometriae Dedicata 2 (1973), 83–99. MR 326574, DOI 10.1007/BF00149284 W. Meyer, Minkowski addition of convex sets, Ph D. Dissertation, University of Wisconsin, Madison, 1969.
- G. C. Shephard, Decomposable convex polyhedra, Mathematika 10 (1963), 89–95. MR 172176, DOI 10.1112/S0025579300003995
- G. C. Shephard, The Steiner point of a convex polytope, Canadian J. Math. 18 (1966), 1294–1300. MR 213962, DOI 10.4153/CJM-1966-128-4
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 190 (1974), 77-86
- MSC: Primary 52A25
- DOI: https://doi.org/10.1090/S0002-9947-1974-0338929-4
- MathSciNet review: 0338929