This unique collection of papers illustrates the connections between origami and a wide range of fields. The papers compiled in this two-part set display the creative melding of origami (or, more broadly, folding) with fields ranging from cell biology to space exploration, from education to kinematics, from abstract mathematical laws to the artistic and aesthetics of sculptural design.

Part 1: Mathematics of origami: Coloring: Coloring connections with counting mountain-valley assignments by T. C. HullColor symmetry approach to the construction of crystallographic flat origami by M. L. A. de las Penas, E. C. Taganap, and T. A. RapanutSymmetric colorings of polypolyhedra by S.-H. Belcastro and T. C. HullMathematics of origami: constructibility: Geometric and arithmetic relations concerning origami by J. Guardia and E. TramunsAbelian and non-abelian numbers via 3D origami by J. I. Royo Prieto and E. TramunsInteractive construction and automated proof in Eos system with application to knot fold of regular polygons by F. Ghourabi, T. Ida, and K. TakahashiEqual division on any polygon side by folding by S. ChenA survey and recent results about commmon developments of two or more boxes by R. UeharaUnfolding simple folds from crease patterns by H. A. Akitaya, Y. Kanamori, Y. Fukui, and J. MitaniMathematics of origami: Rigid foldability: Rigid folding of periodic origami tessellations by T. TachiRigid flattening of polyhedra with slits by Z. Abel, R. Connelly, E. Demaine, M. L. Demaine, T. C. Hull, A. Lubiw, and T. TachiRigidly foldable origami twists by T. A. Evans, R. J. Lang, S. P. Magleby, and L. L. HowellLocked rigid origami with multiple degrees of freedom by Z. Abel, T. C. Hull, and T. TachiScrew-algebra-based kinematic and static modeling of origami-inspired mechanisms by K. Zhang, C. Qiu, and J. S. DaiThick rigidly foldable structures realized by an offset panel technique by B. J. Edmondson, R. J. Lang, M. R. Morgan, S. P. Magleby, and L. L. HowellConfiguration transformation and manipulation of origami cartons by J. S. DaiMathematics of origami: design algorithms: Filling a hole in a crease pattern: Isometric mapping from prescribed boundary folding by E. D. Demaine and J. S. KuSpiderwebs, tilings, and flagstone tessellations by R. J. LangScaling any surface down to any fraction by E. D. Demaine, M. L. Demaine, and K. QaiserCharacterization of curved creases and rulings: Design and analysis of lens tessellations by E. D. Demaine, M. L. Demaine, D. A. Huffmann, D. Koschitz, and T. TachiCurve-folding polyhedra skeletons through smoothing by S. Chandra, S. Bhooshan, and M. El-SayedDesign methods of origami tessellations for triangular spiral multiple tilings by T. Sushida, A. Huzume, and Y. YamagishiA new scheme to describe twist-fold tessellations by T. R. CrainWeaving a uniformly thick sheet from rectangles by E. Davis, E. D. Demaine, M. L. Demaine, and J. RamseyerExtruding towers by serially grafting prismoids by H. Y. ChengOn pleat rearrangements in pureland tessellations by G. KonjevodGraph paper for polygon-packed origami design by R. J. Lang and R. C. AlperinA method to fold generalized bird bases from a given quadrilateral containing an inscribed circle by T. KawasakiPentasia: An aperiodic origami surface by R. J. Lang and B. HayesBase design of a snowflake curve model and its difficulties by U. IkegamiTwo calculations for geodesic modular works by M. KawamuraIndex Part 2: Mathematics of origami: Comparison of compressive properties of periodic non-flat tessellations by Y. Klett, M. Grzeschik, and P. MiddenhorfNumerical analysis of origami structures through modified frame elements by K. Fuchi, P. R. Buskohl, J. J. Joo, G. W. Reich, and R. A. VaiaA study on crash energy absorption ability of lightweight structures with truss core panel by Y. Yang, X. Zhao, S. Tokura, and I. HagiwaraToward optimization of stiffness and flexibility of rigid, flat-foldable origami structures by E. T. Filipov, T. Tachi, and G. H. PaulinoStructural engineering applications of morphing sandwich structures by J. M. Gattas and Z. YouSound-insulting performance of origami-based sandwich trusscore panels by S. Ishida, H. Morimura, and I. HagiwaraThin-walled deployable grid structures by J. Ho and Z. YouDeployable linear folded stripe structures by R. MaleczekGravity and friction-driven self-organized folding by G. H. Filz, G. Grasser, J. Ladinig, and R. MaleczekMagnetic self-assembly of three-dimensional microstructures by E. Iwase and I. ShimoyamaFolding augmented: A design method to integrate structural folding in archietecture by P. D'Acunto and J. J. C. Castellon GonzalezDemands on an adapted design process for foldable structures by S. Hoffmann, M. Barej, B. Gunther, M. Trautz, B. Corves, and J. FeldhusenPlanning motions for shape-memory alloy sheets by M. Ghosh, D. Tomkins, J. Denny, S. Rodriguez, M. Morales, and N. M. AmatoSimple flat origami exploration system with random folds by N. Tsuruta, J. Mitani, Y. Kanamori, and Y. FukuiORICREATE: Modeling framework for design and manufacturing of folded plate structures by R. Chudoba, J. van der Woerd, and J. HeggerRotation erection system (res): Origami extended with cuts by Y. MiyamotoToward engineering biological tissues by directed assembly and origami folding by P. J. Mehner, T. Liu, A. B. Karimi, A. Brodeur, J. Paniagua, S. Giles, P. Richard, A. Nemtserova, S. Liu, R. C. Alperin, S. Bhatia, M. Culpepper, R. J. Lang, and C. LivermoreCosmological origami: Properties of cosmic-web components when a non-stretchy dark-matter sheet folds by M. C. NeyrinckModeling vaults in origami: A bridge between mathematics and architecture by C. Cumino, E. Frigerio, S. Gallina, M. L. Spreafico, and U. ZichOrigami in art, design, and history: Folding perspectives: Joys and uses of 3d anomorhic origami by Y. KlettMaster peace: An evolution of monumental origami by K. Box and R. J. LangWearable metal origami by T. de RuysserCrowdsourcing origami sculptures by J. MoselyOn the aesthetics of folding and technology: Scale, dimensionality, and materiality by M. GardinerComputational problems related to paper crane in the Edo period by J. Maekawa Mitate and origami by H. KoshiroOrigami in education: The kindergarten origametria programme by M. Golan and J. ObermanArea and optimization problems by E. Frigerio and M. L. SpreaficoMathematics and art through the cubotahedron by S.-P. KwanOrigami-inspired deductive threads in pre-geometry by A. TubisUsing paper folding to solve problems in school geometry by H. Yanping and P.-Y. LeeUsing origami to enrich mathematical understanding of self similarity and fractals by A. Bahmani, K. Sharif, and A. HudsonUsing the Fujimoto approximation technique to teach chaos theory to high school students by L. PoladianIndex