Abstract: The present invention relates to a multi-faceted nesting module for building complex geometric structures from a plurality of identical modules. A module includes a body shaped to have faces corresponding with the facial geometry of a three-dimensional lattice made up of tangent polyhedral cells. The module further includes appendages attached to the body and extending only into an adjacent cell of the lattice defined by the body. The appendages have at least one face corresponding with the facial geometry of the three-dimensional lattice but also have cut-away portions where the resulting faces do not interfere with the facial geometry of the three-dimensional lattice.