This is an announcement for the paper "Absorbing angles, Steiner minimal trees, and antipodality" by Horst Martini, Konrad J. Swanepoel, and P. Oloff de Wet. Abstract: We give a new proof that a star $\{op_i:i=1,\dots,k\}$ in a normed plane is a Steiner minimal tree of its vertices $\{o,p_1,\dots,p_k\}$ if and only if all angles formed by the edges at $o$ are absorbing [Swanepoel, Networks \textbf{36} (2000), 104--113]. The proof is more conceptual and simpler than the original one. We also find a new sufficient condition for higher-dimensional normed spaces to share this characterization. In particular, a star $\{op_i: i=1,\dots,k\}$ in any CL-space is a Steiner minimal tree of its vertices $\{o,p_1,\dots,p_k\}$ if and only if all angles are absorbing, which in turn holds if and only if all distances between the normalizations $\frac{1}{\|p_i\|}p_i$ equal $2$. CL-spaces include the mixed $\ell_1$ and $\ell_\infty$ sum of finitely many copies of $R^1$. Archive classification: math.MG math.FA Mathematics Subject Classification: 46B20 (Primary). 05C05, 49Q10, 52A21 (Secondary) Citation: Journal of Optimization Theory and Applications, 143 (2009), The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1108.5046 or http://arXiv.org/abs/1108.5046