double-sided-hexagonal-ring-solid-tetrahedral-symmetry-toroid-20xT4.04a
Those of you who have seen some of my other folded pieces will know that I have been strongly influenced by the designs of Tomoko Fuse. One design in particular, a toroid from page 21 of Fuse's book Unit Polyhedron Origami, (mis)taught me that it was possible to bring together twenty identical objects with tetrahedral symmetry to create a "giant ball." Making these toroids (which, as it turns out, are geometrically invalid near-misses, but most people don't notice that) is always an interesting challenge, and they form an integral part of my repertoire.
A different part of the same book teaches the units depicted in this photograph—the Double-Sided Convex and Concave Hexagonal Ring Solid Units—and page 70 describes how to use the latter to make one of the simplest designs: a truncated cube, or T₄ in the Stewart Toroid nomenclature.
And perhaps now you see where I'm going with this. "Wouldn't it be a lark," I thought to myself, "if I revisited Tomoko Fuse's book in order to combine the tetrahedral symmetry toroid concept with her hexagonal ring solid units?" What you see here is the result.
The coloring is simple: a rainbow gradient from the inside to the outside. Each truncated cube contains 3 red units, 3 orange units, 9 yellow units (shared with neighboring truncated cubes), and 6 green units, after which the cycle reverses: 9 light blue units, 3 dark blue units, and finally 3 purple units. The yellow units are convex Hexagonal Ring Solid units, while all of the other units are concave. The distinction is important: using concave units everywhere by merely reversing their creases where needed causes the structure to easily come apart. Glue doesn't help. Trust me, I tried.
double-sided-hexagonal-ring-solid-tetrahedral-symmetry-toroid-20xT4.04a
Those of you who have seen some of my other folded pieces will know that I have been strongly influenced by the designs of Tomoko Fuse. One design in particular, a toroid from page 21 of Fuse's book Unit Polyhedron Origami, (mis)taught me that it was possible to bring together twenty identical objects with tetrahedral symmetry to create a "giant ball." Making these toroids (which, as it turns out, are geometrically invalid near-misses, but most people don't notice that) is always an interesting challenge, and they form an integral part of my repertoire.
A different part of the same book teaches the units depicted in this photograph—the Double-Sided Convex and Concave Hexagonal Ring Solid Units—and page 70 describes how to use the latter to make one of the simplest designs: a truncated cube, or T₄ in the Stewart Toroid nomenclature.
And perhaps now you see where I'm going with this. "Wouldn't it be a lark," I thought to myself, "if I revisited Tomoko Fuse's book in order to combine the tetrahedral symmetry toroid concept with her hexagonal ring solid units?" What you see here is the result.
The coloring is simple: a rainbow gradient from the inside to the outside. Each truncated cube contains 3 red units, 3 orange units, 9 yellow units (shared with neighboring truncated cubes), and 6 green units, after which the cycle reverses: 9 light blue units, 3 dark blue units, and finally 3 purple units. The yellow units are convex Hexagonal Ring Solid units, while all of the other units are concave. The distinction is important: using concave units everywhere by merely reversing their creases where needed causes the structure to easily come apart. Glue doesn't help. Trust me, I tried.