caa a22 4500 463171462 CHVBK 20180406164814.0 cr unu---uuuuu 170326e20070901xx s 000 0 eng 10.1007/s10998-007-3113-0 doi (NATIONALLICENCE)springer-10.1007/s10998-007-3113-0 Incenter iterations in 3-space [Elektronische Daten] [Gergely Ambrus, András Bezdek] Consider a 3-dimensional point set $$\mathcal{P}$$ which contains the incenters of all the nondegenerate tetrahedra with vertices from $$\mathcal{P}$$ . In this paper we prove that then $$\mathcal{P}$$ is dense in its convex hull. This settles the last unsolved variation in a sequence of similar questions initiated by D. Ismailescu, where he required to include other simplex centers, e.g. the orthocenters or the circumcenters. Our method allows us to generalize the planar incenter problem, showing that the denseness follows from a much weaker assumption for planar point sets. Springer Science+Business Media B.V., 2007 dense point set nationallicence incenter nationallicence iterated process nationallicence Ambrus Gergely Department of Mathematics, University College London, Gower Street, WC1E 6BT, London, UK aut Bezdek András Department of Mathematics and Statistics, Auburn University, 221 Parker Hall, 36849, Auburn, AL, USA aut Periodica Mathematica Hungarica Springer Netherlands 55/1(2007-09-01), 113-119 0031-5303 55:1<113 2007 55 10998 https://doi.org/10.1007/s10998-007-3113-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10998-007-3113-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ambrus Gergely Department of Mathematics, University College London, Gower Street, WC1E 6BT, London, UK aut NATIONALLICENCE 700 1- Bezdek András Department of Mathematics and Statistics, Auburn University, 221 Parker Hall, 36849, Auburn, AL, USA aut NATIONALLICENCE 773 0- Periodica Mathematica Hungarica Springer Netherlands 55/1(2007-09-01), 113-119 0031-5303 55:1<113 2007 55 10998 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer