  Novel extended networks of C8, Si8 and silicon carbide Si4C4 are proposed
based on crystal chemistry rationale and optimized structures to ground state
energies and derived physical properties within the density functional theory
(DFT). The two carbon and silicon allotropes and the silicon carbide belong to
primitive tetragonal space group P-4m2 Number 115. C8 allotrope structure made
of corner sharing C4 and Si4 tetrahedra is illustrated by charge density
projections exhibiting sp3 like carbon hybridization. From careful symmetry
analysis, Symmetry analysis of C8 indicated that it is another representation
of cubic diamond, space group F-d3m Number 227. C8 is identified as ultra-hard
with a similar magnitude of Vickers hardness. The interest in C8 is to serve as
template to study Si8 and Si-C binary. Si8 allotrope is found soft with HV =13
GPa alike cubic Si, and Si4C4 is identified with HV =33 GPa close to
experimental SiC. All three new phases are mechanically (elastic constants) and
dynamically (phonons) stable, and their electronic band structures are
characteristic of insulating C8 (diamond) with large band gaps of about 5 eV,
and semi-conducting Si8 and Si4C4 with band gaps of about 1 eV.
