With the aim of classifying structures into families, a topological representation for crystal types has been proposed using the TopCryst system . Cubic diamond has dia topology and its rare hexagonal form called "lonsdaleite" has lon topology. These two topological types are characteristic of a large number of crystal systems. For example, zinc-blende phases have dia topology and wurtzite phases have lon topology. Recently, a hexagonal tricarbon C 3 allotrope was claimed from ab initio studies to be superdense and superhard with an assigned qtz topology . Later, we proposed qtz C 6 , which is characterized by an ultrahardness comparable (or even superior) to that of diamond . For the sake of completeness, we note that the qtz topology is also adopted by trigonal binary phases .