We introduce and explore two- and three-dimensional lattices formed in Holographic-Polymer Dispersed Liquid Crystals (H-PDLC) materials, which exhibit an electrically controllable index modulation in multiple dimensions. As electro-optically active holograms, these materials exhibit fast dynamic switching phenomena (~100 microseconds), and are simple to fabricate. While many applications have been proposed for these materials, almost all are based on one-dimensional index modulations in various grating regimes. However, constraints in additional dimensions lead to a much greater sensitivity of the polymer morphology to monomer functionality, exposure irradiance, and grating pitch. In an effort to begin to understand this relationship, two-dimensional triangle lattices were created using two monomeric blends exposed over a range of powers. Final diffraction efficiency (Bragg regime), saturation voltage, and polymer morphology were examined from the resulting triangle lattices. Three- dimensional lattices are discussed and a six-beam holographic method is proposed. Photonic crystal applications are envisioned where the pseudo-bandgap can be electrically controlled.