This paper presents geometric texture Wang Tiles to generate geometric textures on different object surfaces at run-time. A set of Wang Tiles is pre-computed from a specific geometric texture and used to generate geometric textures on different object surfaces. Although tile-based approaches are used for image textures, constructing geometric texture Wang Tiles presents additional challenges due to the differences between geometric textures and image textures. The geometric texture Wang Tiles is built automatically by using constrained synthesis to ensure geometric continuity across all possible combinations of tile arrangements. Once a tile set is built, it can be reused for texturing different output objects. This texturing algorithm consumes much less storage and computation than the existing methods.