Park City Mathematics Institute
Geometrical Concepts from Constructions, Models, and Investigations

An Amazing, Space Filling, Non-regular Tetrahedron
by Joyce Frost and Peg Cagle

Go to: background paper and activity
Download: MS Word file

WHAT IS IT?
A background paper and a related classroom activity about tessellating space using the rhombic dodecahedron.

GRADE LEVEL/STRAND
Secondary geometry

CLASS TIME
2 class periods (this would allow enough time for the construction of a group version for each of the three puzzles)

MATERIALS
8.5 by 11 inch paper to fold nets, glue sticks, scissors, file folders, packing tape
optional:
   contact paper
   nets for tetrahedra [view]  [download MS Word file]
   photos of finished models [view]

OBJECTIVES
Increase students' spatial reasoning through the construction and analysis of three related space-filling polyhedral puzzles.

Exploring these shapes can increase understanding of basic concepts of three-dimensional geometry and allow teachers and students to consider ideas such as:

  • How can one think about and use cubes to create other examples of polyhedra that fill space?
  • How can one extend relationships from plane geometry such as the Pythagorean theorem, to three-dimensional space?
  • How can models be constructed and used to explore relationships between space-filling polyhedra?

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    © 2001 - 2009 Park City Mathematics Institute
    IAS/Park City Mathematics Institute is an outreach program of the School of Mathematics
    at the Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540
    Send questions or comments to: Suzanne Alejandre and Jim King

    This material is based upon work supported by the National Science Foundation under Grant No. 0314808.
    Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.