In this paper, we report a construction toy which induces users to recognize the relationship between structures and textures in the three-dimensional (3D) object design. The toy consists of interlocking plastic bricks with textures of geometric patterns that cause visual illusions. The illusions appear more clearly when the blocks with the same texture is assembled and connected. Also, it is demonstrated that the illusions are perceived only within a certain view-angle range to produce appropriate retinal image. Therefore, the toy allows users (i) to make special structures consisting of several types of local structures which induce the illusory perception, and (ii) to consider the range of appropriate viewpoints, where the visual illusions on the surface and the 3D structure cooperatively make the created object look interesting. The validity of this construction toy was confirmed in our workshops during which a wide range of users from children to adults made 3D objects using the toy. It was also demonstrated that participants around ten years old or older could consider and adopt the advantage of illusory textures to construct interesting 3D objects.