Existence of a rigidly foldable reflector gadget

Determine whether a rigidly foldable reflector gadget for pleat-based origami logic exists; specifically, construct or rule out a rigidly foldable crease pattern that, under rigid folding, accepts one input pleat signal and outputs two pleat signals—one identical to the input but with wider pleat width and one negated with equal width—analogous to the reflector gadget used to route and negate signals in flat-folding constructions.

Background

The paper constructs logic components for an origami-based computing scheme using pleat-defined binary states, Bern and Hayes’s NAE clause gadget, and a reflector gadget that duplicates and negates signals. While these gadgets enable a flat-foldable NAND gate, the authors consider whether a fully rigidly foldable computer could be realized.

A major obstacle identified is that no rigidly foldable triangle twist exists, limiting the standard NAE-based approach. Although a rigidly foldable NAE-4 clause gadget is possible, the availability of a rigidly foldable reflector—critical for signal routing, duplication, and negation—remains uncertain. Establishing the existence or non-existence of such a reflector is pivotal for developing rigidly foldable origami logic circuits and, ultimately, a rigidly foldable origami computer.