The special 45°-45°-90° and 30°-60°-90° triangles appear many places in the school curriculum. The baskets described in this paper are good illustrations of the importance of these special triangles, which occur naturally in weaving because of the symmetries enforced by the weave. The baskets also incorporate examples of the relationships between certain solid angles and the angles in the sides that meet to form it. Weavers from cultures throughout the world have used the two and three directional plaiting techniques described. This paper provides detailed descriptions of the structure of these baskets and suggests experiments that students and teachers might do with them in the classroom.