This is an announcement for the paper "Thickness of the unit sphere, $\ell_1$-types, and the almost Daugavet property" by Vladimir Kadets, Varvara Shepelska and Dirk Werner. Abstract: We study those Banach spaces $X$ for which $S_X$ does not admit a finite $\eps$-net consisting of elements of $S_X$ for any $\eps < 2$. We give characterisations of this class of spaces in terms of $\ell_1$-type sequences and in terms of the almost Daugavet property. The main result of the paper is: a separable Banach space $X$ is isomorphic to a space from this class if and only if $X$ contains an isomorphic copy of $\ell_1$. Archive classification: math.FA Mathematics Subject Classification: 46B04 Remarks: To appear in Houston Journal of Mathematics The source file(s), , is(are) stored in gzipped form as with size . The corresponding postcript file has gzipped size . Submitted from: werner@math.fu-berlin.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0902.4503 or http://arXiv.org/abs/0902.4503 or by email in unzipped form by transmitting an empty message with subject line uget 0902.4503 or in gzipped form by using subject line get 0902.4503 to: math@arXiv.org.