The three-dimensional lattice structures disclosed herein have applications including use in medical implants. Some examples of the lattice structure are structural in that they can be used to provide structural support or mechanical spacing. In some examples, the lattice can be configured as a scaffold to support bone or tissue growth. Some examples can use a repeating modified rhombic dodecahedron or radial dodeca-rhombus unit cell. The lattice structures are also capable of providing a lattice structure with anisotropic properties to better suit the lattice for its intended purpose.