We present a framework to generate mesh patterns that consist of a hybrid of both triangles and quads. Given a 3D surface, the generated patterns fit the surface boundaries and curvatures. Such regular and near regular trianglequad hybrid meshes provide two key advantages: First, novel-looking polygonal patterns achieved by mixing different arrangements of triangles and quads together; second, a finer discretization of angle deficits than utilizing triangles or quads alone. Users have controls over the generated patterns in global and local levels. We demonstrate applications of our approach in architectural geometry and pattern design on surfaces.