Design Techniques for Origami Tessellations

0. Origami and Traditional Tessellation Patterns. 0.1. Background of Origami Tessellations. 0.2 Crease Patterns. 0.3 Basic Geometry of Flat-Foldable Crease Patterns. 0.4 Folded State of Crease Patterns. 0.5 Patterns for Twist-Folding. 0.6 Tessellations. 0.7. Tips for Making Beautiful Folds. 1.Folding on Square Grid. 1.1. Square Twist-Patterns. 1.2. Isosceles Right Triangle Twist Pattern. 1.3. Checker Base. 1.4. Changing folded shape. 1.5. Crease patterns as connectable tile. Appendix 1: Pixel Arts Composed of Origami Tessellation. 2. Folding on Equilateral Triangle Grid. 2.1. Equilateral Triangle Twist-Patterns. 2.2. Regular Hexagon Twist-Patterns. 2.3. Right Triangle Twist-Patterns. Column 1: Grid and Twist Pattern. 3. Connecting Triangle Twist Patterns. 3.1. Creating Triangle Twist Patterns. 3.2. Connecting Triangle Twist Patterns. 3.3. Design for Regular Polygon Patterns. Column 02: How to use Triangle Twist Pattern Maker. Appendix 2: Changing Length of Pleat Base. 4.Connecting of Different Base Parts. 4.1. Connectable Side of Boundary. 4.2. Regular Tessellations. 4.3. Tessellation with Equilateral Polygons. 4.4. Combining Crease Patterns Having Different Guide Sides. Appendix 3: Condition that Boundaries are Folded into Similar Shape. 5. Generating Aesthetic Origami Tessellations. 5.1. Origami Tessellations Regarding as Positive-Negative Pattern. 5.2. Parallel Moving Faces by Flat Folding. 5.3. Design for Origami Tessellations Regarding as Positive-Negative Pattern. Appendix 4: Deformation of crease pattern using pleat bases. 6. Folding Bellows. 6.1. Folding Parallel Lines. 6.2. Bent Bellows. 6.3. Periodic Bellows. 6.4. Bending Irregular Bellows. Column 03: Origami Tessellation Design Software "Tess". 7. Application of Twist Pattern Design Method. 7.1. Reconstructing Guide from Given Origami Tessellation. 7.2. Fractal Origami Tessellations and Guides. 7.3. Guide with Gaps. Column 4: Connecting 3D Origami Arts and Origami Tessellations.