origami polytopes - university of...
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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
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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
![Page 3: Origami Polytopes - University of Hawaiisuperm.math.hawaii.edu/_lessons/k_five/lesson_origamiPoly.pdf · The School and University Partnership for Educational Renewal in Mathematics](https://reader030.vdocument.in/reader030/viewer/2022041212/5dd12617d6be591ccb64747b/html5/thumbnails/3.jpg)
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
![Page 4: Origami Polytopes - University of Hawaiisuperm.math.hawaii.edu/_lessons/k_five/lesson_origamiPoly.pdf · The School and University Partnership for Educational Renewal in Mathematics](https://reader030.vdocument.in/reader030/viewer/2022041212/5dd12617d6be591ccb64747b/html5/thumbnails/4.jpg)
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
![Page 5: Origami Polytopes - University of Hawaiisuperm.math.hawaii.edu/_lessons/k_five/lesson_origamiPoly.pdf · The School and University Partnership for Educational Renewal in Mathematics](https://reader030.vdocument.in/reader030/viewer/2022041212/5dd12617d6be591ccb64747b/html5/thumbnails/5.jpg)
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
![Page 6: Origami Polytopes - University of Hawaiisuperm.math.hawaii.edu/_lessons/k_five/lesson_origamiPoly.pdf · The School and University Partnership for Educational Renewal in Mathematics](https://reader030.vdocument.in/reader030/viewer/2022041212/5dd12617d6be591ccb64747b/html5/thumbnails/6.jpg)
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
![Page 7: Origami Polytopes - University of Hawaiisuperm.math.hawaii.edu/_lessons/k_five/lesson_origamiPoly.pdf · The School and University Partnership for Educational Renewal in Mathematics](https://reader030.vdocument.in/reader030/viewer/2022041212/5dd12617d6be591ccb64747b/html5/thumbnails/7.jpg)
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
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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
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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
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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
![Page 11: Origami Polytopes - University of Hawaiisuperm.math.hawaii.edu/_lessons/k_five/lesson_origamiPoly.pdf · The School and University Partnership for Educational Renewal in Mathematics](https://reader030.vdocument.in/reader030/viewer/2022041212/5dd12617d6be591ccb64747b/html5/thumbnails/11.jpg)
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