Numerical simulation of random close packing with tetrahedra

The densest packing of tetrahedra is still an unsolved problem. Numerical simulations of random close packing of tetrahedra are carried out with a sphere assembly model and improved relaxation algorithm. The packing density and average contact number obtained for random close packing of regular tetrahedra is 0.6817 and 7.21 respectively, while the values of spheres are 0.6435 and 5.95. The simulation demonstrates that tetrahedra can be randomly packed denser than spheres. Random close packings of tetrahedra with a range of height are simulated as well. We find that the regular tetrahedron might be the optimal shape which gives the highest packing density of tetrahedra.