Polyhedra Pastimes, the second book in the Investigating Patterns series, allows you to open up your students' minds to the amazing world of polyhedra. Students will transform sheets of paper into cubes and icosahedra. They will enjoy making tetrahedron kites and kaleidocycles. They will learn about Platonic solids not by seeing pictures or models of them, but by actually building them on their own. 

Thirty teacher-friendly activities will enable you to guide your class through topics like Euler's formula, the Golden Ratio, and Archimedean solids. The incorporation of a variety of visual experiences allows students to understand the math and have fun, all at the same time!

Grades 5-8

Available from:


Review in Mathematics Teaching in Middle School
Requires Adobe Adrobat Reader


  1. Regular Polygons and Tessellations
  2. The Regular Polyhedra
  3. From Gumdrops to Zometool®
  4. Regular Polyhedra Nets
  5. Euler’s Formula
  6. Duality and Symmetry
  7. History and Applications
  8. Tetrahedron from an Envelope
  9. No Glue Icosahedron
  10. Pop-Up Dodecahedron
  11. Blow-Up Cube
  12. Skeletal Octahedron
  13. Pyramids and Prisms
  14. The Golden Ratio
  15. Stellations of Regular Polyhedra
  16. Star Building Unit
  17. Origami Stellated Octahedron
  18. Tetrahedron Kite
  19. Polyhedra Bubbles
  20. The Archimedean Solids
  21. Nomenclature
  22. Euler’s Formula Revisited
  23. Filling Space
  24. The Polyhedra of M. C. Escher
  25. An Escher Cuboctahedron
  26. Kaleidocycles
  27. Folding and Unfolding Cubes
  28. Icosahedron Globes
  29. Geodesics
  30. The Buckyball


Extensive educational links on the Internet, in chapter/activity order, may be found at this site to supplement the activities in this book.

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