Robert Fathauer (Joined truncated octahedron)

Joined, ceramic. Commissioned by Glen Whitney for Polyplane.

[36 F, 72 V, 38 E]

This shape fuses two more basic, familiar forms, the cube and octahedron, both Platonic solids. The edges of the original cube are indicated by dotted lines; they have become the long diagonals of twelve of the faces of Joined. On the other hand, the corners of the original octahedron are represented by heavy pyramids, each reminiscent of the corner of an octahedron, in the center of each of the squares formed by the cube edges. (Thus, the triangular facets of each of these eight pyramids are not considered faces of this polyhedron, all of whose faces are quadrilaterals.)

The term “joined” in the geometric description of this piece (and echoed in its title, although perhaps there with additional connotations) refers to a modification of a given shape that replaces each of its edges with a rhombus. A lovely “geometric identity” among three-dimensional shapes and such modifications performed on them tells us that if you start with a cube, add a pyramid to each face, and then perform this “join” operation, you end up with precisely this same polyhedron. In other words, the geometric description of this sculpture could just as well have been “joined elevated cube.”