A toy brick system is provided having a plurality of bricks each of which has a post extending from first end of a body of the brick and having a socket at a second end. The post in each brick in the plurality is engageable with a socket of an adjacently place brick in a removable rotational engagement enabling curved and angled configuration of assembled structures. Engagement and disengagement from the rotational engagement can only occur at a specific engagement angle between adjacent bricks thereby maintaining the rotational engagement of adjacent bricks once engaged and rotated out of the engagement angle. The bricks are configurable in a linear fashion or with curved exterior walls for forming curved structures.