A variation on Hamiltonian cycles in graphs are found in—or can be applied to—designs in a variety of art forms such as dance and educational kinesthetic activities, polyrhythms, lace shirtwaist buttons, paths of billiard balls in polygons, Celtic knots, and string figures. We examine a variety of what may be idiomatically called pseudo–Hamiltonian tours, but which we are describing as {n/(a₁, a_{2, a3,..., am) designs. We suggest some applications, with special attention to their use in embodied mathematics movement explorations. These designs can help provide crossover points for visual and movement artists and mathematicians to make connections between their fields.}