To provide a structure of a curtain wall having a polygonal wall surface which enables arbitrary change of a break angle in a prescribed angular range.

In s structure of a polygonal wall surface in a curtain wall constituted by disposing square-frame-shaped curtain wall units CU adjacently, projecting pieces 31c, 31d... directed to the sides of curtain wall longitudinal frames 31B and 31A made adjacent are formed on the outer surfaces of the longitudinal frames 31A and 31B of the curtain wall units CU, between the units CU adjacent horizontally, and each of the curtain wall units CU is disposed in a state of having a break angle in plan view, while an interposition member 32 for a break angle part having overlapping member pieces 32b, 32c and 32d being in the condition of stretching over the projecting pieces 31c, 31d... of the longitudinal frames is disposed in the part of mating surfaces of the right and left longitudinal frames 31A and 31B. Airtightness and watertightness are ensured by overlapping parts of the projecting pieces of the right and left longitudinal frames 31A and 31B and the overlapping member pieces 32b, 32c... of the interposition member 32 for the break angle part.