Show how all three solids have the same basic symmetry. The cubeoctahedron can be constructed mathematically by connecting the midpoints of the edges of a cube, or by connecting the midpoints of the edges of an octahedron. A cubeoctahedron is formed naturally by the close packing of spheres. You can make one by glueing marbles together. The diamond Diamond crystal consists of interlocking hexagons with an underlying tetrahedral symmetry.
Construction Begin by having students construct a tetrahedron.
Have the students take out one gumdrop and four toothpicks. Ask them to stick the toothpicks in the gumdrop so that the ends of the toothpick are as far apart as possible, as if they repel each other. This is a model of the bonds in a carbon atom. Students tend to keep the toothpicks in one plane. Show them that they can get the toothpicks further apart if they think in three dimensions.