Tutorial to Make a Polyhedra Origami Paper Figure

Fold three-dimensional polyhedra from paper patterns.

A polyhedron is a three-dimensional shape with polygons for sides or faces. Polyhedra can be regular, meaning the faces are all identical, or irregular, meaning the faces differ from each other. Students of math and geometry sometimes construct paper polyhedra to help them understand the underlying principles of their field of study. Others make paper polyhedra just because it is enjoyable. You can make your own paper polyhedron with shapes ranging from simple to complex.

Things You'll Need

• Graph paper
• Pencil
• Ruler
• Crayons or markers
• Scissors
• Tape

Instructions

1. Draw a square on a sheet of graph paper using a ruler. Draw four more squares equal in size to the first square. Construct the four new squares so that each shares a side with the original square.

2. Draw one more square equal in size to the rest. Draw it so that it shares one side with only one of the squares surrounding the original square. The six squares should now form a cross shape that is the pattern for your polyhedron.

3. Decorate or color the pattern with crayons or markers if you desire. Another way to have a colored polyhedron is to use colored paper for printing it.

4. Cut the paper around the perimeter of the cross figure, but do not cut any of the squares apart from each other.

5. Fold the adjoining edges of all the squares into 90-degree angles so that the squares form a cube. Now you have a basic regular polyhedron with squares for faces.

Tips & Warnings

• You can use heavier cardstock for constructing the pattern. This heavier paper helps the polyhedron maintain its shape once it is taped. You can make more complex polyhedra by using shapes with more sides such as pentagons, hexagons, and so forth. The more sides the face of the polyhedron has, the more faces it will have as well. If you have trouble envisioning how to draw the adjoining faces, you can first construct a polyhedron out of separate pieces of paper that make up the faces. Use removable tape to secure the edges. After it is assembled, remove the tape and flatten the polyhedron into a pattern without detaching any of the faces. Trace around this pattern onto another sheet of paper, cut it out, fold it, and assemble it into an identical polyhedron. Teachers can use paper polyhedron construction as a classroom activity to help students learn geometry and mathematics.

References

• George Hart: Paper Polyhedra
• Isotropic: Archimedean Polyhedra
• Tom Gettys: Polyhedral Solids
• Korthalsaltes: Paper Models of Polyhedra
• University of California: Models of Regular Polyhedra

Resources

• George Hart: Slide-Together Polyhedrons