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Pop-Up Geometry:

The Mathematics behind Pop-Up Cards

© Joseph O'Rourke 2021—2023

Cambridge University Press. xii+129 pages, 143 figures. March 2022.

Amazon paperback link

ISBN 978-1-009-09840-3 Hardback
ISBN 978-1-009-09626-3 Paperback

Pop-Up Animated GIFs

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All animations were made with Mathematica.

Chapter 1
Parallel Folds
Letter T
Recursive Rhomb
Chapter 2
V-fold Median
Y-Motion & Sphere Sc
(3 MB)
Rotary Motion
Rotary Motion (top view)
Chapter 3
Knight's Visor
Knight's Visor geometry
(2 MB)
Chapter 4
Pop-Up Spinner [Akira Nishihara]
Minimal Spinner
Chapter 5
Cube Flattening
Cube 180
Cube180 Arcs
Cube 90
Octahedron Tracks
Pop-up Regular Tetrahedron
Two Tetrahedra
Chapter 6
Linkage Shear 2D
Polygon 2D [ADD+13]
Nested V 4-chains
Orthogonal Polyhedron [ADD+13]

[ADD+13]: Abel, Z. R., E. D. Demaine, M. L. Demaine, S. C. Eisenstat, A. Lubiw, A. Schulz, D. L. Souvaine, G. Viglietta, and A. Winslow (2013). Algorithms for designing pop-up cards. In 30th Internat. Symp. Th. Aspects Comp. Sci. (STACS), Volume 20, pp. 269–280. Schloss Dagstuhl Publishing. Link to paper.

Pop-Up Card Templates

Click on the thumbnail to download a PDF of the template.

Chapter 1
Parallel Folds Fig.1.4 p.4
Angled Cuts Fig.1.10 p.9
Parallel Unequal Fig.1.11 p.9
Three Parallel Cuts Fig.1.12 p.10
Slanted Parallel Fig.1.13 p.10
Letter T Fig.1.14 p.11
Cylinder Fig.1.18 & 8.1 p.13 & 108
Chapter 2
V-Fold Fig.2.1 p.16
Y-Motion Fig.2.9 p.24
Rotation Circle Fig.2.16 p.29
Chapter 3
Knight's Visor Fig.3.4 p.33
Chapter 4
Pop-up Spinner Fig.4.2 p.48
Spinner Cuts Fig.4.3 p.49
Minimal Spinner Fig.4.15 p.58