Fig. 4: Mirroring, translating, and gluing of crease patterns.
From: Algorithmic design of origami mechanisms and tessellations
a Mirroring operation. Crease pattern graph (auxiliary vertices shown) with marked mirror vertices and folded configuration of corresponding crease pattern before and after the application of the mirror operation. b Translating operation. Crease pattern graph (with auxiliary vertices) with marked translation vector (defined by the two connected vertices) and folded configuration after application of the translation operation. c Example structure obtained by translating operation. d Example (kirigami) structure obtained by mirroring operation where the mirror vertices form a line. e Scheme to tessellate patterns using the mirroring operation. f Example structure obtained with scheme in Fig. 4e with non-parallel mirror planes. g Example structure obtained by applying the scheme in Fig. 4e in two directions. h Structure obtained by applying the scheme in Fig. 4e on the square twist pattern. i Tessellation obtained by repeated application of the mirroring and translating operation. The structure belongs to a well-documented family4. j Gluing operation. Unfolded configuration of two crease patterns before application of the operation, unfolded and folded configuration after application of the gluing operation. k Example structure obtained by repeated application of the gluing operation. l Example structure obtained by the application of quadrilateral-closing, mirroring and gluing operation.
