Tetragonal and hexagonal pentacarbon allotropes tet-C 5 . Recently, the body-centered tetragonal carbon allotrope C 4 (tet-C 4 ) in the space group I-4m2 (No. 119) (Fig. ) has been proposed to serve as a template for the design of the related phases. The four atoms of the unit cell are detailed in Table , considering the structure in simple tetragonal arrangement. The subsequent transformation into C 5 consists in keeping the body center carbon (C1 at ½, ½, ½), which becomes in C(1c) Wyckoff position (follow the transformation arrows), as well as the two C2, whereby C2a and C2b become C3(2g) and the z coordinate becomes z′ instead of ¼. The additional carbon C2 is provided by parameterizing the z position of C1b, resulting in a two-fold C2 (2e) at 0, 0, z. After full geometry relaxation, the resulting structure retains the tetragonal symmetry now resolved in space group P-4m2 (No. 115). The structure is shown in Fig. with colored spheres corresponding to the three carbon sites given by the coordinates in Table , i.e. with well determined z = 0.854 and zʹ = 0.314.