Cephoids: Minkowski sums of de Gua simplexes

Pallaschke D, Rosenmüller J (2010)
OPTIMIZATION 59(4): 515-540.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
Within this article we discuss the structure of those polytopes in [image omitted] which are Minkowski sums of de Gua simplexes. A de Gua simplex is the convex hull of the origin and n positive multiples of the unit vectors (see [J.J. Gray, Algebra in geometry from Newton to Plucker (German), Math. Semesterberichte 36 (1989), pp. 175-204.]). We characterize these polytopes by describing the shape of their (outward) faces. Given some notion of 'nondegeneracy' or 'general position' for our polytopes, we present a recursive procedure that yields all maximal faces. Also, we derive a formula indicating the number of maximal faces, which depends on the dimension and the number of de Gua simplexes involved only.
Stichworte
Minkowski sum; cephoids; cylinders; de Gua simplexes; tentacles
Erscheinungsjahr
2010
Zeitschriftentitel
OPTIMIZATION
Band
59
Ausgabe
4
Seite(n)
515-540
ISSN
0233-1934
eISSN
1029-4945
Page URI
https://pub.uni-bielefeld.de/record/1795875

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Pallaschke D, Rosenmüller J. Cephoids: Minkowski sums of de Gua simplexes. OPTIMIZATION. 2010;59(4):515-540.
Pallaschke, D., & Rosenmüller, J. (2010). Cephoids: Minkowski sums of de Gua simplexes. OPTIMIZATION, 59(4), 515-540. https://doi.org/10.1080/02331930801951280
Pallaschke, D., and Rosenmüller, Joachim. 2010. “Cephoids: Minkowski sums of de Gua simplexes”. OPTIMIZATION 59 (4): 515-540.
Pallaschke, D., and Rosenmüller, J. (2010). Cephoids: Minkowski sums of de Gua simplexes. OPTIMIZATION 59, 515-540.
Pallaschke, D., & Rosenmüller, J., 2010. Cephoids: Minkowski sums of de Gua simplexes. OPTIMIZATION, 59(4), p 515-540.
D. Pallaschke and J. Rosenmüller, “Cephoids: Minkowski sums of de Gua simplexes”, OPTIMIZATION, vol. 59, 2010, pp. 515-540.
Pallaschke, D., Rosenmüller, J.: Cephoids: Minkowski sums of de Gua simplexes. OPTIMIZATION. 59, 515-540 (2010).
Pallaschke, D., and Rosenmüller, Joachim. “Cephoids: Minkowski sums of de Gua simplexes”. OPTIMIZATION 59.4 (2010): 515-540.
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