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Susan Working
Mathematics Professor
Email: susan.working@gcccd.edu
Phone: 619-644-7290

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Building an Icosahedron

This project will allow students to be hands-on in building a platonic solid. It is a good project to do after solids are covered in your class. Your students will already know about regular polygons and they may even be able to derive on their own that there are only 5 platonic solids. Have them start with equilateral triangles and see if they can figure out how many objects they could possibly build and then move on to squares, pentagons, and then hexagons, etc. It is easiest to have the students try and figure out many how faces they could possibly have come together at one vertex to build a solid. Working with angles they should derive that it is impossible to build a solid with n-sided polygons where .

Applicable Courses

Geometry

Background

Regular Polygons, Angles, Polyhedra

Materials needed

  • Pushpins (every student in your class will need one)
  • 30 toothpicks (with sharp edges at each end) per student (extras are a good idea since they break or some have blunt ends)
  • Tubing – I use windshield washer tubing (vinyl or rubber). It generally comes in a length of 6 feet. You will need to cut the tubing into about 1/3 inch pieces. 6 feet should be enough for 18 students. It is very inexpensive to buy at an auto parts store.

The project can be completed in one class period (50 minutes). It is fun and the students have something to take home with them at the end of the class. It is also great to display their icosahedra for open house!

You can let the students who have excellent fine motor skills stellate their icosahedron – it is very time-consuming, but a beautiful object.

Icosahedron Worksheet

Last Updated: 10/06/2014

Contact

Susan Working
Mathematics Professor
Email: susan.working@gcccd.edu
Phone: 619-644-7290

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