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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    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.