We present RFIBricks, an interactive building block system based on ultrahigh frequency radio-frequency identification (RFID) sensing. The system enables geometry resolution based on a simple yet highly generalizable mechanism: an RFID contact switch, which is made by cutting each RFID tag into two parts, namely antenna and chip. A magnetic connector is then coupled with each part. When the antenna and chip connect, an interaction event with an ID is transmitted to the reader. On the basis of our design of RFID contact switch patterns, we present a system of interactive physical building blocks that resolves the stacking order and orientation when one block is stacked upon another, determines a three-dimensional (3D) geometry built on a two-dimensional base plate, and detects user inputs by incorporating electromechanical sensors. Because it is calibration-free and does not require batteries in each block, it facilitates straightforward maintenance when deployed at scale. Compared with other approaches, this RFID-based system resolves several critical challenges in human-computer interaction, such as 1) determining the identity and the built 3D geometry of passive building blocks, 2) enabling stackable token+constraint interaction on a tabletop, and 3) tracking in-hand assembly.