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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Indecomposable polytopes
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by Walter Meyer PDF
Trans. Amer. Math. Soc. 190 (1974), 77-86 Request permission


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.
    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
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 190 (1974), 77-86
  • MSC: Primary 52A25
  • DOI:
  • MathSciNet review: 0338929