The continuous emergence of large-scale freeform architectures brings crucial challenges to the design and manufacture of such structures because of their complex geometries. Accordingly, geometric rationalization with the goal of efficient fabrication becomes a core research topic of architectural geometry. We explore the geometric rationalization for freeform architecture by some particular structures and surfaces achieved with the help of optimization algorithms and their underlying geometry insights. (1) Shading and lighting systems are torsion-free structures with planar beams based on quad meshes. They satisfy certain functionality requirements such as preventing light from going inside a building as shading systems or reflecting light into a building as lighting systems. (2) Freeform honeycomb structures are constructed based on hex-dominant meshes with a planar beam mounted along each edge and beams intersect without torsion at each node with same angles between any two neighbors. (3) Polyhedral patterns covering freeform surfaces only with planar faces are specified to fulfill certain aesthetics requirements. (4) Space frame structures consist of two types of components: nodes and struts. Rationalization of node and strut structures aims at minimizing production cost and ensuring stability as a functional constraint.