tag:blogger.com,1999:blog-6555947.post112710515168353161..comments2014-01-12T10:46:48.153-07:00Comments on The Geomblog: Holes in Sets: The ConclusionSuresh Venkatasubramaniannoreply@blogger.comBlogger2125tag:blogger.com,1999:blog-6555947.post-1127598183367789222005-09-24T15:43:00.000-06:002005-09-24T15:43:00.000-06:00--What's the story in 3-d? Are there arbitrarily l...--What's the story in 3-d? Are there arbitrarily large point sets for which the convex hull of any 5 points is a tetrahedron? <BR/><BR/><BR/>No. Let S be any d+3 points in general position from R^d. Then there exists a subset S' of S of cardinality d+2 such that the convex hull of S' contains no point of S' in its interior. <BR/><BR/><BR/><BR/><BR/> <BR/><BR/><A></A><A></A>Posted by<A><B> </B></A>AnonymousAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-6555947.post-1127151611313289912005-09-19T11:40:00.000-06:002005-09-19T11:40:00.000-06:00That's very nice. What's the story in 3-d? Are t...That's very nice. What's the story in 3-d? Are there arbitrarily large point sets for which the convex hull of any 5 points is a tetrahedron? <BR/><BR/> <BR/><BR/><A></A><A></A>Posted by<A><B> </B></A>AnonymousAnonymousnoreply@blogger.com