Negative linear compressibility, i.e., the phenomenon of expansion rather than shrinkage in at least one direction upon the application of a hydrostatic compressive pressure is an unusual techanical property which is attracting more interest in the recent years. Here, through analysis of published data by Hu et al. [J. Superhard Mater. 36, 257–269 (2014)] as well as through static force-field based simulations, it is shown that it is possible to achieve this property in the novel carbon allotropes built from sp2 and sp3 hybridized carbon atoms which have a two-dimensional projection that resembles a honeycomb motif in their (001) plane. This is in accordance with earlier predictions that honeycombs deforming through a hinging-like mechanism could exhibit this property for certain geometries.