Additive manufacturing (AM, also known as 3D printing) can produce novel three-dimensional structures using low-loss dielectric materials. This enables the construction of dielectrics with complex shapes that enable innovative microwave applications such as resonators, filters, and metamaterial lenses. This paper addresses the production and characterization of cellular structures of various designed densities created with a low loss ceramic material, alumina (aluminum oxide), via vat photopolymerization. The permittivity of these printed structures is variable over roughly an octave, with a range of relative permittivites from 1.78 to 3.60, controlled via part geometry.