This is an announcement for the paper "Diameter 2 properties and convexity" by Trond A. Abrahamsen, Peter Hajek, Olav Nygaard, Jarno Talponen, and Stanimir Troyanski. Abstract: We present an equivalent midpoint locally uniformly rotund (MLUR) renorming $X$ of $C[0,1]$ on which every weakly compact projection $P$ satisfies the equation $\|I-P\| = 1+\|P\|$ ($I$ is the identity operator on $X$). As a consequence we obtain an MLUR space $X$ with the properties D2P, that every non-empty relatively weakly open subset of its unit ball $B_X$ has diameter 2, and the LD2P+, that for every slice of $B_X$ and every norm 1 element $x$ inside the slice there is another element $y$ inside the slice of distance as close to 2 from $x$ as desired. An example of an MLUR space with the D2P, the LD2P+, and with convex combinations of slices of arbitrary small diameter is also given. Archive classification: math.FA Mathematics Subject Classification: 46B04, 46B20 Remarks: 15 pages Submitted from: trond.a.abrahamsen@uia.no The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1506.05237 or http://arXiv.org/abs/1506.05237