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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 with tetrahedral, octahedral or cubic symmetries. Fourteen such DRTs will completely enclose one in their center.
This 3D model was created with vzome.
A physical model can be made from 32 balls and 60 red struts available from zometool.
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