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The Mathematics of Origami

© Joseph O'Rourke 2025

Cambridge University Press

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Chapter 4: Flat Folding is Hard
Fig. 4.6
Wire Splitter Gadget (500K)
Fig. 4.15
Triangle Twist Splitter Gadget(1MB)


Chapter 5: Rigid Origami and Degree-4 Vertices
Fig. 5.1
Open Box (1.8MB)
Fig. 5.3
Loop Table (Instagram link)
Fig. 5.10
Miura map fold (1MB)
Fig. 5.12
Miura Tessellation 85deg (1.5MB)
Fig. 5.16
Miura-unit 60deg (700KB)
Fig. 5.22
SquareTwist-unit 1Vertex (1.3MB)
Fig. 5.23
SquareTwist 4Vertices (1.5MB)
Fig. 5.25
SquareTwist Tessellation (2.5MB)
Fig. 5.26
Octahedron Top (1MB)


Chapter 6: Origami Design
Fig. 6.6
Rabbit Ear Molecule (1Mb)


Chapter 7: Fold & 1-Cut
Fig. 7.16
Cube Flattening (1.5Mb)


Chapter 9: Sef-Folding Origami
Fig. 9.6, 9.8
Degree-6 vertex folding (Mode 1) (1.2Mb)

Templates

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Chapter 2: Stamp Folding
Fig. 2.13(a)
3 x 2 Map
Fig. 2.14 4 x 2 Map


Chapter 3:Single Vertex Folds
Fig. 3.2a, 3.4a
Degree-8 vertex
Fig. 3.3c Not Flat Foldable
Fig. 3.6 Local Min
Fig. 3.7 Local Min Tie
Fig. 3.8 Kawasaki's Theorem
Fig. 3.11b Kawasaki's: Recutting


Chapter 4: Flat Folding is Hard
Fig. 4.3
Not Flattenable
Fig. 4.5a
Splitter Gadget
Fig. 4.14a
TriangleTwist Gadget


Chapter 5: Rigid Origamie and Degree-4 Vertices
Fig. 5.4
Loop Table
Fig. 5.10
Miura 3x2 Tessellation
Fig. 5.19a
Square Twist (a): M^4
Fig. 5.19b
Square Twist (b): M^2V^2
Fig. 5.22
Square Twist Tessellation


Chapter 6: Origami Design
Fig. 6.5a
Waterbomb base
Fig. 6.5b
Waterbomb crease pattern
Fig. 6.14a
Sawhorse molecule
Fig. 6.15b
Pentagon template
Fig. 6.16c
Uniaxial crease pattern


Chapter 7: Fold & 1-Cut
Fig. 7.1
Houdini Star
Fig. 7.6
Nonconvex Pentagon
Fig. 7.8
Turtle Straight Skeleton


Chapter 8: Curved Crease Origami
Fig. 8.4
Vessica Piscis
Fig. 8.7c
Nested Squares
Fig. 8.8a
Nested Circles


Chapter 9: Self-Folding Origami
Fig. 9.1b
Waterbomb Tube


Chapter 10: Origamizer
Fig. 10.13a
Degree-4 Vertex Tuck