caa a22 4500 46798932X CHVBK 20180323112540.0 cr unu---uuuuu 170328e19900601xx s 000 0 eng 10.1007/BF01302928 doi (NATIONALLICENCE)springer-10.1007/BF01302928 Facets with fewest vertices [Elektronische Daten] [A. Bezdek, K. Bezdek, E. Makai Jr., P. McMullen] Forv>d≧3, letm(v, d) be the smallest numberm, such that every convexd-polytope withv vertices has a facet with at mostm vertices. In this paper, bounds form(v, d) are found; in particular, for fixedd≧3, $$\frac{{r - 1}}{r} \leqslant \mathop {\lim \inf }\limits_{\upsilon \to \infty } \frac{{m(\upsilon ,d)}}{\upsilon } \leqslant \mathop {\lim \sup }\limits_{\upsilon \to \infty } \frac{{m(\upsilon ,d)}}{\upsilon } \leqslant \frac{{d - 3}}{{d - 2}}$$ , wherer=[1/3(d+1)]. Springer-Verlag, 1990 Bezdek A. Mathematical Institute, Hungarian Academy of Sciences, Pf. 127, H-1364, Budapest V, Hungary aut Bezdek K. Department of Geometry, Eötvös Lórand University, Rákóczi ut 5, H-1088, Budapest, Hungary aut Makai Jr. E. Mathematical Institute, Hungarian Academy of Sciences, Pf. 127, H-1364, Budapest V, Hungary aut McMullen P. Department of Mathematics, University College London, Gower Street, WC1E 6BT, GB-London, UK aut Monatshefte für Mathematik Springer-Verlag 109/2(1990-06-01), 89-96 0026-9255 109:2<89 1990 109 605 https://doi.org/10.1007/BF01302928 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01302928 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bezdek A. Mathematical Institute, Hungarian Academy of Sciences, Pf. 127, H-1364, Budapest V, Hungary aut NATIONALLICENCE 700 1- Bezdek K. Department of Geometry, Eötvös Lórand University, Rákóczi ut 5, H-1088, Budapest, Hungary aut NATIONALLICENCE 700 1- Makai Jr E. Mathematical Institute, Hungarian Academy of Sciences, Pf. 127, H-1364, Budapest V, Hungary aut NATIONALLICENCE 700 1- McMullen P. Department of Mathematics, University College London, Gower Street, WC1E 6BT, GB-London, UK aut NATIONALLICENCE 773 0- Monatshefte für Mathematik Springer-Verlag 109/2(1990-06-01), 89-96 0026-9255 109:2<89 1990 109 605 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer