0
Research Papers

Reconstructing David Huffman's Origami Tessellations1

[+] Author and Article Information
Eli Davis

e-mail: ebdavis@mit.edu

Erik D. Demaine

e-mail: edemaine@mit.edu

Martin L. Demaine

e-mail: mdemaine@mit.edu

Jennifer Ramseyer

e-mail: ramseyer@mit.edu
MIT CSAIL,
Cambridge, MA 02139

1A preliminary version of this paper appears in the ASME 2013 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE 2013).

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the Journal of Mechanical Design. Manuscript received February 1, 2013; final manuscript received September 3, 2013; published online October 8, 2013. Assoc. Editor: Larry L. Howell.

J. Mech. Des 135(11), 111010 (Oct 08, 2013) (7 pages) Paper No: MD-13-1052; doi: 10.1115/1.4025428 History: Received February 01, 2013; Revised September 03, 2013

David A. Huffman (1925–1999) is best known in computer science for his work in information theory, particularly Huffman codes, and best known in origami as a pioneer of curved-crease folding. But during his early paper folding in the 1970s, he also designed and folded over a 100 different straight-crease origami tessellations. Unlike most origami tessellations designed in the past 20 years, Huffman's straight-crease tessellations are mostly three-dimensional, rigidly foldable, and have no locking mechanism. In collaboration with Huffman's family, our goal is to document all of his designs by reverse-engineering his models into the corresponding crease patterns, or in some cases, matching his models with his sketches of crease patterns. Here, we describe several of Huffman's origami tessellations that are most interesting historically, mathematically, and artistically.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Huffman, D. A., 1976, “Curvature and Creases: A Primer on Paper,” IEEE Trans. Comput., 25(10), pp. 1010–1019. [CrossRef]
Pope, L., 2012, Origami: Art + Mathematics. Exhibit, Eloise Pickard Smith Gallery, University of California, Santa Cruz, CA.
Demaine, E. D., Demaine, M. L., and Koschitz, D., 2010, “Reconstructing David Huffman's Legacy in Curved-Crease Folding,” Origami5: Proceedings of the 5th International Conference on Origami in Science, Mathematics and Education, Singapore, P. Wang-Iverson, R. J. Lang, and M. Yim, eds., A K Peters, Natick, MA, pp. 39–52.
Lister, D., “Tessellations, Origami Mailing List Posting,” Available at http://britishorigami.info/academic/lister/tessel.php
Lister, D., “When did Origami Tessellations Begin? Origami Mailing List Posting,” http://britishorigami.info/academic/lister/tessel_begin.php
Resch, R. D. “Self-Supporting Structural Unit Having a Series of Repetitious Geometric Modules,” U. S. Patent No. 3,407,558, filed Jan. 24, 1966, patented Oct. 29, 1968.
Gjerde, E., 2008, Origami Tessellations: Awe-Inspiring Geometric Designs, Singapore, A K Peters, Natick, MA.
Lang, R. J., and Bateman, A., 2010, “Every Spider Web has a Simple Flat Twist Tessellation,” Origami5: Proceedings of the 5th International Conference on Origami in Science, Mathematics and Education (OSME 2010), Singapore, P. Wang-Iverson, R. J. Lang, and M. Yim, eds., A K Peters, pp. 449–454.
Demaine, E. D., Demaine, M. L., and Ku, J., 2010, “Folding any Orthogonal Maze,” Origami5: Proceedings of the 5th International Conference on Origami in Science, Mathematics and Education (OSME 2010), Singapore, P. Wang-Iverson, R. J. Lang, and M. Yim, eds., A K Peters, pp. 449–454.

Figures

Grahic Jump Location
Fig. 1

David Huffman's drawing of an origami tessellation crease pattern (date unknown) in which the triangle is nearly equilateral after being rounded to have corners on a square grid. Used with permission of the Huffman family.

Grahic Jump Location
Fig. 2

Our photograph of David Huffman's design “three axis woven design” (date unknown), which was the basis of our reconstruction

Grahic Jump Location
Fig. 3

Points and lines of interest in Fig. 2 for reconstructing Huffman's “three axis woven design”

Grahic Jump Location
Fig. 4

Step-by-step partial reconstructions of Huffman's “three axis woven design”

Grahic Jump Location
Fig. 5

David Huffman's hand-drawn crease pattern for his design “three axis woven design” shown in Fig. 2. Used with permission of the Huffman family.

Grahic Jump Location
Fig. 6

Our reconstruction of David Huffman's “three axis woven design.”

Grahic Jump Location
Fig. 7

The components of a repeating unit

Grahic Jump Location
Fig. 8

The twist to make “pinwheels”

Grahic Jump Location
Fig. 9

Enlarging the nodes of “extruded boxes”

Grahic Jump Location
Fig. 10

The Vanes family tree

Grahic Jump Location
Fig. 11

Our reconstruction of David Huffman's origami tessellation (title and date unknown), which we call “Waterbombs”

Grahic Jump Location
Fig. 12

Our reconstruction of David Huffman's origami tessellation (title and date unknown), which we call “Exdented boxes”

Grahic Jump Location
Fig. 13

Our reconstruction of David Huffman's origami tessellation (title and date unknown), which we call “extruded boxes”

Grahic Jump Location
Fig. 14

Our reconstruction of David Huffman's origami tessellation (title and date unknown), which we call “pinwheels”

Grahic Jump Location
Fig. 15

Our reconstruction of David Huffman's “raised Vanes, both vertical and horizontal” (date unknown)

Grahic Jump Location
Fig. 16

Our reconstruction of David Huffman's “rectangular woven design” (date unknown)

Grahic Jump Location
Fig. 17

Our reconstruction of David Huffman's “squares with legs” (date unknown)

Grahic Jump Location
Fig. 18

Our reconstruction of David Huffman's origami tessellation (title and date unknown), which we call “stars-triangles”

Grahic Jump Location
Fig. 19

Our reconstruction of David Huffman's origami tessellation (title and date unknown), which we call “tessellation of doom”

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In