The discovery of building blocks offers new opportunities to develop and control properties of extended solids. Compounds with fluorite-type Bi2O2 blocks host various properties including lead-free ferroelectrics and photocatalysts. In this study, we show that triple-layered Bi2MO4 blocks (M = Bi, La, Y) in Bi2MO4Cl allow, unlike double-layered Bi2O2 blocks, to extensively control the conduction band. Depending on M, the Bi2MO4 block is truncated by Bi-O bond breaking, resulting in a series of n-zigzag chain structures (n = 1, 2, infinity for M = Bi, La, Y, respectively). Thus, formed chain structures are responsible for the variation in the conduction band minimum (-0.36 to -0.94 V vs SHE), which is correlated to the presence or absence of mirror symmetry at Bi. Bi2YO4Cl shows higher photoconductivity than the most efficient Bi2O2-based photocatalyst with promising visible-light photocatalytic activity for water splitting. This study expands the possibilities of thickening (2D to 3D) and cutting (2D to 1D) fluorite-based blocks toward desired photocatalysis and other functions.