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Build a Crystal The Rhombic Dodecahedron

Build a Crystal The Rhombic Dodecahedron. NCTM, 3-22-07 Al Mendle ammendle@ucdavis.edu http://trc.ucdavis.edu/almendle. A rhombic dodecahedron is a polyhedron with twelve congruent rhombic faces. Each face is proportional to the dimensions shown in the diagram.

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Build a Crystal The Rhombic Dodecahedron

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  1. Build a CrystalThe Rhombic Dodecahedron NCTM, 3-22-07 Al Mendle ammendle@ucdavis.edu http://trc.ucdavis.edu/almendle

  2. A rhombic dodecahedron is a polyhedron with twelve congruent rhombic faces. Each face is proportional to the dimensions shown in the diagram.

  3. attach a square based pyramid to each face of a cube. The height of the pyramid should be the length of the edge of the cube. One way to visualize how a rhombic dodecahedron is formed is to: make a 3-dimensional “cross” with seven cubes. Connect the centers of outside cubes Another way to generate a rhombic dodecahedron is to:

  4. Could bees be geometers? The hexagonal cells of a honeycomb are when looked at in 3-dimensions are filling space in way way that is very close to a tiling of rhombic dodecahedra.

  5. Some Useful Websites • http://www.answers.com/topic/rhombic-dodecahedron • http://mathforum.org/pcmi/hstp/resources/rhombic/ • http://www.ellison.com/creativeideas/?p=printer_friendly&idea=4895 • http://www.johnrausch.com/PuzzlingWorld/chap08.htm • http://www.johnrausch.com/PuzzlingWorld/chap08b.htm • http://www.devon.gov.uk/dcs/maths/shapes/module17.htm • http://mathworld.wolfram.com/RhombicDodecahedron.html

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