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? *