This is how to build 5 tetrahedra on a dodecahedron. In the Zometool geometry, if a cube can fit into a dodecahedron, then a tetrahedron can too! This is a way to build a beautiful, multi-chiral model. This model uses the Green Lines. A finished model can use only the GreenLines kit, but to build like in these instructions, it takes extra Blue struts such as can be found in a Creator 1 kit. 

You can find more models that use the GreenLines here.