The properties and applications of auxetics have been widely explored in the past years. Through proper utilization of auxetic structures, designs with unprecedented mechanical and structural behaviors can be produced. Taking advantage of this, we present the development of novel and lowcost 3D structures inspired by a simple auxetic unit. The core part, which we call the body in this paper, is a 3D realization of 2D rotating squares. This body structure was formed by joining four similar structures through softer material at the vertices. A monolithic structure of this kind is accomplished through a custom-built multi-material 3D printer. The model works in a way that, when torque is applied along the face of the rotational squares, they tend to bend at the vertex of the softer material, and due to the connected-ness of the design, a proper opening and closing motion is achieved. To demonstrate the potential of this part as an important component for robots, two applications are presented: a soft gripper and a crawling robot. Vacuum-driven actuators move both the applications. The proposed gripper combines the benefits of two types of grippers whose fingers are placed parallel and equally spaced to each other, in a single design. This gripper is adaptable to the size of the object and can grasp objects with large and small cross-sections alike. A novel bending actuator, which is made of soft material and bends in curvature when vacuumed, provides the grasping nature of the gripper. Crawling robots, in addition to their versatile nature, provide a better interaction with humans. The designed crawling robot employs negative pressure-driven actuators to highlight linear and turning locomotion.