Does [Tverberg's theorem](http://en.wikipedia.org/wiki/Tverberg%27s_theorem) hold for CAT(0) spaces of covering dimension $d<\infty$: 


Is it true that for any $d$-dimensional $CAT(0)$-space $X$ and a subset $E\subset X$ of cardinality $(d + 1)(r - 1) + 1$, there exists a point $x\in X$ and a partition of $E$ into $r$ subsets $E\_1,...,E\_r$, such that $x$ belongs to the intersection of closed convex hulls of the subsets $E\_i$? 



Tverberg's theorem in CAT(0) spaces
No. Let $X$ be a tripod (three segments with one common endpoint), $d=1$, $r=2$ and $E$ the set of the 3 leaf points.


