Another initial search protocol lies in crystal chemistry rationale calling for structure engineering. Recently, body-centered tetragonal bct-C 4 (Figure ) was proposed by us in space group I m2 as the simplest three-dimensional (3D) carbon network; but it was evidenced as featuring another representation of diamond. Nevertheless bct-C 4 was conceived to serve as seed starting template to building other original carbon allotropes . The removal of the body center carbon as schematized with the red arrow leads to simple tetragonal structure with eight tetrahedra occupying the corners of the structure. The space group symmetry is lowered and becomes identified as P m2. The usefulness of resulting C 3 is to serve as template structure with the empty space left by central carbon removal, leaving room for interstitials. Beside bct-C 4 recovered with one tetrahedral sp 3 , i.e., C(tet.), two, and three carbon interstitials enter as trigonal (sp 2 ) C(trig.) atoms modifying the tetrahedral diamondlike edifice significantly and bringing new structure-properties relationships. Such investigations constitute the aim of this paper through the study of the electronic, mechanical, and dynamic properties. Specifically, while the insertion of two trigonal carbons leading to C 5 was recently studied (Fig. ) with the outcome of stable ultrahard carbon allotrope, we focus our present work on the insertion of three carbon atoms giving C 6 stoichiometry, i.e., 3 C(tet.) and 3 C(trig.) as schematized in Fig. with colored spheres, i.e., red and yellow for the two types of C(trig.).