Strongly monotypic polytopes in R3

• Autorzy: Borowska D. , Grzybowski J.
• Języki publikacji: EN

Abstrakty

EN

McMullen et al. [3] characterized all three-dimensional monotypic polytopes by presenting four types of such polytopes. They stated that three of these types are strongly monotypic polytopes. We examine which monotypic polytopes of the fourth type are strongly monotypic. This way we complete the description of all strongly monotypic polytopes in R3.

Słowa kluczowe

EN

Minkowski sum; summands of compact convex sets

PL

suma Minkowskiego; zwarty zbiór wypukły; topologia algebraiczna

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2008
• Tom: Vol. 41, nr 1
• Strony: 165--169
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Borowska D.

autor

Grzybowski J.

• Faculty of Mathematics and Computer Science Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland,

Bibliografia

• [1] D. Borowska, J. Grzybowski, Sallee's sets in Rn, to appear.
• [2] H. Maehara, Convex bodies forming pairs of constant width, J. Geom. 22 (1984), 101-107.
• [3] P. McMullen, R. Schneider, G. C. Shephard, Monotypic potytopes and their intersection properties, Geom. Dedicata 3 (1974), 99-129.
• [4] D. Paliaschke, R. Urbański, Pairs of Compact Convex Sets, Fractional Arithmetic with Convex Sets, Serie Mathematics and Its Applications, vol. 548, Kluwer Academic Publisher 2002, Dortrecht-Boston-London.
• [5] G. T. Sallee, Pairs of sets of constant relative width, J. Geometry 29 (1987).
• [6] R. Schneider, Convex Bodies: The Brunn-Minkowski Theory, Encyclopedia of Mathematics and its Applications, Vol 44. Cambridge Univ. Press 1993.