Small Triakis Octahedron Stellations

R. Whorf found that there are probably several thousand stellations of the small triakis octahedron (Wenninger 1983, p. 36). In particular, the convex hulls of the great cubicuboctahedron , the Archimedean great rhombicuboctahedron , and great rhombihexahedron are all the Archimedean truncated cube , whose dual is the small triakis octahedron, so the duals of these solids (i.e., the great hexacronic icositetrahedron, great deltoidal icositetrahedron, and great rhombihexahedron) are all stellations of the small triakis octahedron (Wenninger 1983, p. 57).

The stellation diagram showing the lines of intersections of nonparallel face planes with the plane of one face are shown above (left figure). Note that the diagram appearing in Wenninger (1989, p. 38, Fig. 28) corresponds to just the central "star" portion (right figure).