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

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

Secondary geometry

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

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

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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    This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. 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.