Dessins d’enfants, also called hypermaps, are closely associated with ramified coverings of the Riemann sphere—what a layperson may prefer to think of as seamless wallpaperings of other closed surfaces with copies of the Earth’s surface (Earth serving in lieu of the Riemann sphere.) Dessins d’enfants have been a focus of interest in recent years in fields as challenging as number theory and quantum gravity. Let’s add basketmaking to the list. I show that Strobl’s clever knotology weaving technique—which realizes curved surfaces in plain tabby weave by using straight (but folded) weaving elements—suffices to make models of the Riemann surfaces encoded by dessins d’enfants. These baskets can be folded up into a single stack of triangles—an echo of a Riemann surface being a ramified covering of the sphere. Plans and weaving instructions are provided for an example the reader can make.