#MathArtChallenge 97: Tomoko Fusé’s Bird Tetrahedron Origami

The Challenge: Make an origami sculpture using Tomoko Fusé’s text Multidimensional Transoformations Unit Orgiami. (I used instructions on pgs 134, 138-139.)

Materials Needed: Paper (origami paper is handy, but any paper will work) and scissors/paper cutter.
Math Concepts: 3 dimensional building, angles, space filling, rotations, proportions

I love this particular type of origami because you get to determine the shape and scope of the final piece. You’ve basically made yourself some origami legos. If you have a lot of time, you’ll be able to fill space (well, there’ll be holes) with this unit & connectors, and could therefore, theoretically build a really dramatic sculpture, much like one could also do with legos. Just this is with paper!
For mine, I opted for the relatively simple tripe helix with a double rainbow. It took about 8 hours of folding and construction. We’re all a ways a way from this, but someday, post-pandemic, this would be a REALLY lovely project to do as a whole class or in groups.

To build this sculpture, you need square paper, scissors and 3 different folds:

  • Bird tetrahedron (technically a di-triangular pyramid)
    • 3 pieces of nxn square paper per di-triangular pyramid.
  • Horizontal connectors.
    • If your bird units are made with nxn paper, these are n/4 x n/2 paper. (1/8th the area of the nxn paper) 2 connectors needed to connect each 2 bird units. 6 needed to connect 3 units.
  • Vertical connectors.
    • If your bird units are made with nxn paper, these are n/2 squares. (or 1/4th of the original nxn paper) 3 connectors will connect 2 bird units.

Folding the bird units:

Putting the bird units together:

Folding the horizontal connectors:

Putting bird units together horizontally:

Folding the vertical connectors:

Putting bird units together vertically:

Questions to consider:

  • What forms are possible? What are excluded?
  • How much space is actually taken up?
  • Is it possible to get a square grid going here? A cubic one?
  • How many transformations are actually happening?
  • How many triangles appear in each of the tetrahedral units?
    • Each di-pyramid is actually 3 square faces folded along their diagonal to make 2 45-45-90 triangles. What do you notice about that construction? What might it tell you about the angles between the faces?

Depending on how you use this activity, you may engage with different standards. Here are a few suggestions for how you might integrate the 8 mathematical practices. Feel free to add your own suggestions in the comments!

6.) Attend to precision. (This gets pretty annoying if you’re not at least working toward being precise when folding.)

7.) Look for and make use of structure. How can these units be put together? What is possible and what is not?

8.) Look for and express regularity in repeated reasoning What do you notice about how the pieces do and do not fit together? What generalities can we determine?

Author: Annie Perkins

Math Teacher in Minneapolis, MN.

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