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

Rhombic Dodecahedron - Hidden Within or
Surrounding the Cube?

Joyce Frost and Kris Koch

Teacher Directions || Worksheet
MS Word Downloads:     rhombic.doc || worksheet.doc
PDF Downloads:     rhombic.pdf || worksheet.pdf || SRDnets.pdf || hinges.pdf

Classroom activity illustrating the interconnections between a cube and a rhombic dodecahedron.

Secondary geometry

1-2 class periods


  • Teacher classroom set of Zome™ tools (if available)
  • If Zome™ tools are not available, each group of 4 students could use 96 clear standard sized drinking straws (24 for each person) and blue and yellow curling ribbon to build a total of 12 square pyramids per group.
  • Student worksheet


  • Increase students' and teachers' understanding of important geometrical concepts through the construction and analysis of three-dimensional models.
  • Analyze and compare properties of the cube and its corresponding rhombic dodecahedron by dissecting and transforming the solid cube.
  • Develop mathematical arguments about geometric relationships of the cube and its corresponding rhombic dodecahedron.
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    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

    With program support provided by Math for America

    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.