origami polytopes - university of...

The School and University Partnership for Educational Renewal in MathematicsAn NSF-funded Graduate STEM Fellows in K–12 Education ProjectUniversity of Hawai‘i at Manoa, Department of Mathematics

Origami Polytopes

Origami Polytopes

This is a guide to building polytopes (in particular polyhedra) with paper squares. This is intended to be used tosupplement other lessons. For example, this can used to learn about geometry, shapes, polytopes, symmetry,and dimensions to .

Instructions

UHM Department of Mathematicssuperm.math.hawaii.edu

1 Robert YoungGrade Level: 3-12

The School and University Partnership for Educational Renewal in MathematicsAn NSF-funded Graduate STEM Fellows in K–12 Education ProjectUniversity of Hawai‘i at Manoa, Department of Mathematics

Open previous fold

UHM Department of Mathematicssuperm.math.hawaii.edu

2 Robert YoungGrade Level: 3-12

The School and University Partnership for Educational Renewal in MathematicsAn NSF-funded Graduate STEM Fellows in K–12 Education ProjectUniversity of Hawai‘i at Manoa, Department of Mathematics

Open previous folds

UHM Department of Mathematicssuperm.math.hawaii.edu

3 Robert YoungGrade Level: 3-12

The School and University Partnership for Educational Renewal in MathematicsAn NSF-funded Graduate STEM Fellows in K–12 Education ProjectUniversity of Hawai‘i at Manoa, Department of Mathematics

UHM Department of Mathematicssuperm.math.hawaii.edu

4 Robert YoungGrade Level: 3-12

The School and University Partnership for Educational Renewal in MathematicsAn NSF-funded Graduate STEM Fellows in K–12 Education ProjectUniversity of Hawai‘i at Manoa, Department of Mathematics

UHM Department of Mathematicssuperm.math.hawaii.edu

5 Robert YoungGrade Level: 3-12

The School and University Partnership for Educational Renewal in MathematicsAn NSF-funded Graduate STEM Fellows in K–12 Education ProjectUniversity of Hawai‘i at Manoa, Department of Mathematics

Flip and rotate

UHM Department of Mathematicssuperm.math.hawaii.edu

6 Robert YoungGrade Level: 3-12

The School and University Partnership for Educational Renewal in MathematicsAn NSF-funded Graduate STEM Fellows in K–12 Education ProjectUniversity of Hawai‘i at Manoa, Department of Mathematics

Open folds from previous two steps

You are now done with one polytope piece! You need to make a total of 6 pieces to make a cube. Afterassembling a cube, try to make a stellated octahedron (12 pieces), or a stellated icosahedron (30 pieces).

UHM Department of Mathematicssuperm.math.hawaii.edu

7 Robert YoungGrade Level: 3-12

The School and University Partnership for Educational Renewal in MathematicsAn NSF-funded Graduate STEM Fellows in K–12 Education ProjectUniversity of Hawai‘i at Manoa, Department of Mathematics

When you’ve made enough pieces, please note that each piece has two “pockets” and two “hands.”

Let’s put our pieces together to form a cube. To do so, we follow three simple rules.

Rule number 1: Pockets face outside.

This is wrong!

UHM Department of Mathematicssuperm.math.hawaii.edu

8 Robert YoungGrade Level: 3-12

The School and University Partnership for Educational Renewal in MathematicsAn NSF-funded Graduate STEM Fellows in K–12 Education ProjectUniversity of Hawai‘i at Manoa, Department of Mathematics

Rule number 2: Hands are outside.

This is wrong!

When you satisfy rules 1 and 2, it should look like this.

UHM Department of Mathematicssuperm.math.hawaii.edu

9 Robert YoungGrade Level: 3-12

The School and University Partnership for Educational Renewal in MathematicsAn NSF-funded Graduate STEM Fellows in K–12 Education ProjectUniversity of Hawai‘i at Manoa, Department of Mathematics

Now you’re ready for the final rule.Rule number 3: Stick one hand in each pocket.

That’s it! Now you have everything you need to make your own polytopes. For shapes that are morecomplex than the cube, you’ll have to be more creative about where the joints of the pieces bend. Howeverrules 1-3 still apply.

UHM Department of Mathematicssuperm.math.hawaii.edu

10 Robert YoungGrade Level: 3-12

The School and University Partnership for Educational Renewal in MathematicsAn NSF-funded Graduate STEM Fellows in K–12 Education ProjectUniversity of Hawai‘i at Manoa, Department of Mathematics

UHM Department of Mathematicssuperm.math.hawaii.edu

11 Robert YoungGrade Level: 3-12