Geometrical effects on folding of macromolecules are investigated using linear chains with tetrahedral structure and hard-core interactions among its monomers; extra self-avoidance, namely, nontopological neighbor, is also considered. Our results were obtained by exact calculations using chains with small number N of monomers (up to 16) and by Monte Carlo simulation, using the ensemble growth method (EGM), for larger N. For some cases we provide a comparative study using two types of lattice and three different models. The original number of angle choices, zeta=3 (coordination number), is shown to be effectively reduced to zeta(eff)=2.760, and the radius of gyration and end-to-end distance, for finite chains (N less than or equal to 140), scales with the number of monomers as N-nu, where nu congruent to 2/3. This is significantly larger than the corresponding value for the self-avoiding walk model, nu congruent to 0.6. The relative frequency of monomer pair contacts was obtained by the exact Gibbs ensemble, involving all possible configurations. The same calculation using the EGM reveals ergodic difficulties; its significance on the setting up of pathways for folding of macromolecules is discussed.