We construct 2Ω(n 5/4) combinatorial types of triangulated 3-spheres on n vertices. Since by a result of Goodman and Pollack (1986) there are no more than 2O(n logn) combinatorial types of simplicial 4-polytopes, this proves that asymptotically, there are far more combinatorial types of triangulated 3-spheres than of simplicial 4-polytopes on n vertices. This complements results of Kalai (1988)...

Abstract Developable Surfaces can be manufactured starting from the unrolled geometry without tearing or stretching. You use different materials, but you must apply forces to turn 2D planar shape into 3D design structure. Our main goal is define a computational model simulate and control this process.

The molecular geometry of complex of adenine with 8 water molecules was calculated with Hartree-Fock (HF). The standard 6-31G(d) basis set has been employed. The existence of C-H…O Hydrogen bonds between the water molecules and the hydrophobic part of nucleobase is stablished. We optimized structures and computed interaction energies of all complexes of adenine with water molecules step by step...