How to make a paper Icosahedron

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A icosahedron is a 20-sided shaped.
A icosahedron is a 20-sided shaped. (Image: images from wikimedia and from the UMN's Geometry Center)

Making a icosahedron, a 20-sided shaped, out of paper is a fun project for kids or adults.

Things You'll Need

  • thick paper
  • scissors
  • whole punch
  • string or twist ties

Cut out 20 equilateral triangles from thick paper. The bigger your triangles the bigger your final icosahedron. Try and make all your triangles exactly the same; making and using a template is good idea. The more uniform your triangles the better your final icosahedron will fit together.

Equilateral Triangle  - has all 60 degree angles
Equilateral Triangle - has all 60 degree angles

Using the hole punch, punch holes into the three ends of each triangle. Try and punch the holes in the same spot in triangle, and don't punch too close to the end of the paper.

Punch holes in the corners
Punch holes in the corners

Using the string or twist ties, connect four triangles together to a create a parallelogram. Repeat this 4 times - so you will have 5 parallelograms total.

Connect the parallelograms together by the middle triangles. See attached image (from the Geometry Center - UMN).

How to attach all the triangles together
How to attach all the triangles together

Carefully "roll" up the triangles and attach them all together to get your icosahedron! Enjoy!

The final shape!
The final shape!

Tips & Warnings

  • Try to make as perfect a equilateral triangle as possible as your template.
  • You can color the pieces to make it more decorative
  • The Geometry Center, part of the University of Minnesota is a great place to go for more Math Fun
  • You may find out that math is fun and vindicate your grade school math teacher's dorky proclamations.

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