We present Plesio-Bricks, a geometric modeling framework to generate 3-dimensional space-filling shapes for the design of topologically interlocking architectured materials. Our modeling approach is based on the generalization of the concept of three-dimensional Plesiohedra. These are convex space-filling shapes generated using Voronoi tessellations of space based on symmetrically arranged points (formally known as symmetric Delone/Delaunay sets) as Voronoi sites. Our key insight is that using lines as our Voronoi sites and arranging them according to the isometries of a cube, we can obtain convex shapes that afford interlocking interactions with neighboring shapes. Previous works primarily demonstrated topological and geometrical interlocking systems in 2.5-dimensional space, meaning they often lie on a singular plane and have a planar top or bottom surface. In contrast to this, our framework offers a systematic, and more importantly, parametrizable approach for creating truly volumetric interlocking. In this work, we study one of many such parametrizations by considering the effect of non-convexity (and therefore interlocking) based on the arrangement and length of line-sites. We conduct a preliminary numerical evaluation of the influence of this parametrization on the mechanical characteristics of the resultant structure.