Dimpled Rhombic Triacontahedron - Construction

I've recently discovered a delightful new space filling polyhedron. For lack of a better name, I'm calling it a "Dimpled Rhombic Triacontahedron" (hereafter DRT). As the name implies, the DRT is generated by making "dimples" in a rhombic triacontahedron. The four dimples result from removing one golden rhombohedron from each of four vertices having tetrahedral symmetry as shown. The DRT is chiral, meaning that either a "left handed" or "right handed" version can be made depending which tetrahedral set of vertices are selected for the dimples. DRTs can be packed to form a [lattice](https://skfb.ly/QyOF) with tetrahedral, octahedral or cubic symmetries. Fourteen such DRTs will completely enclose one in their center. This 3D model was created with [vzome](http://www.vzome.com). A physical model can be made from 32 balls and 60 red struts available from [zometool](http://www.zometool.com).