The Mathematics of Origami
© Joseph O'Rourke 2025
© Joseph O'Rourke 2025
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Chapter 4: Flat Folding is Hard |
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Fig. 4.6 |
Wire Splitter Gadget (500K) |
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Fig. 4.15 |
Triangle Twist Splitter Gadget(1MB) |
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Chapter 5: Rigid Origami and Degree-4 Vertices |
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Fig. 5.1 |
Open Box (1.8MB) |
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Fig. 5.3 |
Loop Table (Instagram link) |
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Fig. 5.10 |
Miura map fold (1MB) |
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Fig. 5.12 |
Miura Tessellation 85deg (1.5MB) |
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Fig. 5.16 |
Miura-unit 60deg (700KB) |
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Fig. 5.22 |
SquareTwist-unit 1Vertex (1.3MB) |
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Fig. 5.23 |
SquareTwist 4Vertices (1.5MB) |
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Fig. 5.25 |
SquareTwist Tessellation (2.5MB) |
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Fig. 5.26 |
Octahedron Top (1MB) |
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Chapter 6: Origami Design |
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Fig. 6.6 |
Rabbit Ear Molecule (1Mb) |
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Chapter 7: Fold & 1-Cut |
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Fig. 7.16 |
Cube Flattening (1.5Mb) |
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Chapter 9: Self-Folding Origami |
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Fig. 9.6, 9.8 |
Degree-6 vertex folding (Mode 1) (1.2Mb) |
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Click on the thumbnail to download a PDF of the template.
Chapter 2: Stamp Folding |
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Fig. 2.13(a) |
3 x 2 Map |
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| Fig. 2.14 | 4 x 2 Map |
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Chapter 3:Single Vertex Folds |
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Fig. 3.2a, 3.4a |
Degree-8 vertex |
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| Fig. 3.3c | Not Flat Foldable |
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| Fig. 3.6 | Local Min |
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| Fig. 3.7 | Local Min Tie |
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| Fig. 3.8 | Kawasaki's Theorem |
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| Fig. 3.11b | Kawasaki's: Recutting |
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Chapter 4: Flat Folding is Hard |
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Fig. 4.3 |
Not Flattenable |
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Fig. 4.5a |
Splitter Gadget |
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Fig. 4.14a |
TriangleTwist Gadget |
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Chapter 5: Rigid Origamie and Degree-4 Vertices |
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Fig. 5.4 |
Loop Table |
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Fig. 5.10 |
Miura 3x2 Tessellation |
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Fig. 5.19a |
Square Twist (a): M^4 |
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Fig. 5.19b |
Square Twist (b): M^2V^2 |
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Fig. 5.22 |
Square Twist Tessellation |
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Chapter 6: Origami Design |
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Fig. 6.5a |
Waterbomb base |
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Fig. 6.5b |
Waterbomb crease pattern |
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Fig. 6.14a |
Sawhorse molecule |
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Fig. 6.15b |
Pentagon template |
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Fig. 6.16c |
Uniaxial crease pattern |
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Chapter 7: Fold & 1-Cut |
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Fig. 7.1 |
Houdini Star |
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Fig. 7.6 |
Nonconvex Pentagon |
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Fig. 7.8 |
Turtle Straight Skeleton |
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From How To Fold It |
Turtle with perpendiculars |
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Chapter 8: Curved Crease Origami |
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Fig. 8.4 |
Vessica Piscis |
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Fig. 8.7c |
Nested Squares |
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Fig. 8.8a |
Nested Circles |
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Chapter 9: Self-Folding Origami |
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Fig. 9.1b |
Waterbomb Tube |
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Chapter 10: Origamizer |
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Fig. 10.13a |
Degree-4 Vertex Tuck |
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