The primative cell (P) has fractional lattice points at the corners of the cell, and the base-centered cell (C) has additional fractional lattice points at the center of the basal planes of the unit ...

The lattice points are touching one another but not in the most efficient way. In other words, we are creating a lot of empty space between the atoms. In order to generate the simple cubic structure, ...

Because of this, the second layer will only cover half of the holes in the first layer. pattern shown here. Since I realize that it is difficult to pin point the actual unit cell from the lattice, let ...

The lattice of the hexagonal close packed crystal is hexagonal and a basis of two atoms is placed in the same orientation on each lattice point. The diagrams below illustrate the geometry and space ...

He studies convex and discrete geometry, with a focus on the theory of lattice-point enumeration in polyhedra and its applications to algebraic geometry, representation theory, and geometric invariant ...