Keizo Ushio's sculptures, split tori and Möbius bands
Nathaniel A. Friedman, Carlo H. Séquin · Journal of Mathematics and the Arts · 2007
Keizo Ushio is a leading international stone sculptor whose work has introduced split tori and Möbius bands to the world on a grand scale. Starting with a simple circular torus or with more elaborate twisting bands, he drills a large number of closely spaced holes to form two strands, which may or may not be connected, depending on the overall rotation of the cutting void. In the case of a torus with a 360-degree rotation of the cut, he obtains two twisted, tangled loops, which can be re-arranged in an ingenious way to form a dramatic figure-of-eight configuration. Keizo's split loop sculptures are reviewed and classified by the topological and geometrical rules that govern how toroidal structures can be split in a regular way. The basic concepts related to these shapes are clarified and explained with computer-generated renderings and through stylized plastic maquettes built on a rapid prototyping machine. These models are also used to explore possible generalizations of the underlying splitting paradigm and to realize configurations that could not easily be carved from stone.