Materials and Methods: Embroidery with pearl cotton on thread-wrapped styrofoam balls
Designer & Artist: Carolyn Yackel
Consider cutting all the corners off of a cube in such a way that the resulting faces are regular octagons. The former eight vertices have become eight equilateral triangles. The final solid is called a truncated cube. Alternatively, deeper cuts could have been made at each corner so that the cuts connected midpoints of adjacent edges. In that case, the resulting faces would have been smaller (rotated) squares. The eight removed vertices would still have revealed eight equilateral triangles. The resulting solid this time is a cuboctahedron. This piece shows five truncated Platonic solids projected onto the sphere: the truncated cube, the cuboctahedron, the truncated tetrahedron, the truncated octahedron, and the icosadodecahedron. Two more of the Archimedean solids can be obtained by truncation from Platonic solids. The artist's chapter "Symmetries in Temari" in Crafting by Concepts, eds. belcastro and Yackel, deals with the issues of truncation and temari techniques in depth. In addition, very detailed instructions are given in the chapter for making the navy blue truncated cube ball with yellow triangular motifs and red flowers occupying the octagons.